Alright, the following works. @user16217248 got me started. See the discussion under that answer.

How to safely and efficiently find abs((int)num1 - (int)num2)

/// Safely and efficiently return `abs((int)num1 - (int)num2)`
unsigned int abs_num1_minus_num2_int(int num1, int num2)
{
    unsigned int abs_diff = num1 > num2 ?
        (unsigned int)num1 - (unsigned int)num2 :
        (unsigned int)num2 - (unsigned int)num1;

    return abs_diff;
}

The secret is to do the num1 > num2 ternary comparison with signed integer values, but then to reinterpret cast them to unsigned integer values to allow for well-defined overflow and underflow behavior when getting the absolute value of num1 - num2.

Here is my full test code:

absolute_value_of_num1_minus_num2.c from my eRCaGuy_hello_world repo:

///usr/bin/env ccache gcc -Wall -Wextra -Werror -O3 -std=gnu17 "$0" -o /tmp/a -lm && /tmp/a "$@"; exit
// For the line just above, see my answer here: https://stackoverflow.com/a/75491834/4561887

#include <limits.h>
#include <stdbool.h> // For `true` (`1`) and `false` (`0`) macros in C
#include <stdint.h>  // For `uint8_t`, `int8_t`, etc.
#include <stdio.h>   // For `printf()`


#define TEST_EQ(func, num1, num2, equals) \
    printf("%s\n", func((num1), (num2)) == (equals) ? "Passed" : "FAILED")

/// Safely and efficiently return `abs((int8_t)num1 - (int8_t)num2)`
uint8_t abs_num1_minus_num2_int8(int8_t num1, int8_t num2)
{
    // Note: due to implicit type promotion rules, rule 2 in my answer here
    // (https://stackoverflow.com/a/72654668/4561887) applies, and both the `>`
    // comparison, as well as subtraction, take place below as `int` types.
    // While signed `int` overflow and underflow is undefined behavior, none of
    // that occurs here.
    // - It's just useful to understand that even though we are doing
    //   `(uint8_t)num1 -(uint8_t)num2`, the C compiler really sees it as this:
    //   `(int)(uint8_t)num1 - (int)(uint8_t)num2`.
    // - This is because all small types smaller than `int`, such as `uint8_t`,
    //   are first automatically implicitly cast to `int` before any
    //   mathematical operation or comparison occurs.
    // - The C++ compiler therefore sees it as this:
    //   `static_cast<int>(static_cast<unsigned char>(num1)) - static_cast<int>(static_cast<unsigned char>(num2))`.
    //   - Run this code through https://cppinsights.io/ to see that.
    //     See here: https://cppinsights.io/s/bfc425f6 --> and click the play
    //     button.
    uint8_t abs_diff = num1 > num2 ?
        (uint8_t)num1 - (uint8_t)num2 :
        (uint8_t)num2 - (uint8_t)num1;

    // debugging
    printf("num1 = %4i (%3u); num2 = %4i (%3u); num1-num2=%3u;  ",
        num1, (uint8_t)num1, num2, (uint8_t)num2, abs_diff);

    return abs_diff;
}

/// Safely and efficiently return `abs((int)num1 - (int)num2)`
unsigned int abs_num1_minus_num2_int(int num1, int num2)
{
    unsigned int abs_diff = num1 > num2 ?
        (unsigned int)num1 - (unsigned int)num2 :
        (unsigned int)num2 - (unsigned int)num1;

    // debugging
    printf("num1 = %11i (%10u); num2 = %11i (%10u); num1-num2=%10u;  ",
        num1, (unsigned int)num1, num2, (unsigned int)num2, abs_diff);

    return abs_diff;
}


int main()
{
    printf("Absolute difference tests.\n");

    // ---------------
    // int8_t types
    // ---------------

    int8_t num1_8;
    int8_t num2_8;

    printf("\n");
    printf("INT8_MIN = %i, INT8_MAX = %i\n", INT8_MIN, INT8_MAX); // -128, 127

    num1_8 = -7;
    num2_8 = -4;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 3);

    num1_8 = INT8_MIN;
    num2_8 = INT8_MAX;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, UINT8_MAX);

    num1_8 = INT8_MAX;
    num2_8 = INT8_MIN;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, UINT8_MAX);

    num1_8 = 100;
    num2_8 = 10;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 90);

    num1_8 = 10;
    num2_8 = 100;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 90);

    num1_8 = 10;
    num2_8 = 10;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 0);

    num1_8 = INT8_MAX;
    num2_8 = 1;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 126);

    num1_8 = 1;
    num2_8 = INT8_MAX;
    TEST_EQ(abs_num1_minus_num2_int8, num1_8, num2_8, 126);

    // ---------------
    // int types
    // ---------------

    int num1;
    int num2;

    printf("\n");
    printf("INT_MIN = %i, INT_MAX = %i\n", INT_MIN, INT_MAX); // -2147483648, 2147483647

    num1 = -7;
    num2 = -4;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 3);

    num1 = INT_MIN;
    num2 = INT_MAX;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, UINT_MAX);

    num1 = INT_MAX;
    num2 = INT_MIN;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, UINT_MAX);

    num1 = 100;
    num2 = 10;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 90);

    num1 = 10;
    num2 = 100;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 90);

    num1 = 10;
    num2 = 10;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 0);

    num1 = INT_MAX;
    num2 = 1;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 2147483646);

    num1 = 1;
    num2 = INT_MAX;
    TEST_EQ(abs_num1_minus_num2_int, num1, num2, 2147483646);


    return 0;
}

Sample run and output:

eRCaGuy_hello_world/c$ ./absolute_value_of_num1_minus_num2.c
Absolute difference tests.

INT8_MIN = -128, INT8_MAX = 127
num1 =   -7 (249); num2 =   -4 (252); num1-num2=  3;  Passed
num1 = -128 (128); num2 =  127 (127); num1-num2=255;  Passed
num1 =  127 (127); num2 = -128 (128); num1-num2=255;  Passed
num1 =  100 (100); num2 =   10 ( 10); num1-num2= 90;  Passed
num1 =   10 ( 10); num2 =  100 (100); num1-num2= 90;  Passed
num1 =   10 ( 10); num2 =   10 ( 10); num1-num2=  0;  Passed
num1 =  127 (127); num2 =    1 (  1); num1-num2=126;  Passed
num1 =    1 (  1); num2 =  127 (127); num1-num2=126;  Passed

INT_MIN = -2147483648, INT_MAX = 2147483647
num1 =          -7 (4294967289); num2 =          -4 (4294967292); num1-num2=         3;  Passed
num1 = -2147483648 (2147483648); num2 =  2147483647 (2147483647); num1-num2=4294967295;  Passed
num1 =  2147483647 (2147483647); num2 = -2147483648 (2147483648); num1-num2=4294967295;  Passed
num1 =         100 (       100); num2 =          10 (        10); num1-num2=        90;  Passed
num1 =          10 (        10); num2 =         100 (       100); num1-num2=        90;  Passed
num1 =          10 (        10); num2 =          10 (        10); num1-num2=         0;  Passed
num1 =  2147483647 (2147483647); num2 =           1 (         1); num1-num2=2147483646;  Passed
num1 =           1 (         1); num2 =  2147483647 (2147483647); num1-num2=2147483646;  Passed

Adjacently related

1. The "absolute subtraction" above reminds me of the "rounding divide" set of solutions you can do with integer math too. For that, see my other answer here: Rounding integer division (instead of truncating). I present rounding up, rounding down, and rounding to nearest when doing integer division.

See also

1. My answer on implicit casting/promotion and Integer and floating point rank and promotion rules in C and C++
2. https://cppinsights.io/ - a very useful tool which expands your C++ code into exactly what the compiler sees, including after applying all automatic implicit type promotion rules in the compiler.
   1. Ex: see my code above here: https://cppinsights.io/s/bfc425f6 --> then click the play button to convert and expand it into what the compiler sees.

The standard C library is providing the optimized solutions for many problems with considerations based on the architecture, compiler in use and others. The abs() function defined in stdlib.h is one of these, and it is used for your purpose exactly. To emphasize the point, here is ARM compiler result when using abs vs a version of a homebrew abs: https://arm.godbolt.org/z/aO7t1n

Paste:

#include <stdio.h>
#include <stdlib.h>

int main(void)
{
    srand(111);
    int x = rand() - 200;
    printf("%d\n", abs(x));
}

results in

main:
        push    {r4, lr}
        mov     r0, #111
        bl      srand
        bl      rand
        sub     r1, r0, #200
        cmp     r1, #0
        rsblt   r1, r1, #0
        ldr     r0, .L4
        bl      printf
        mov     r0, #0
        pop     {r4, pc}
.L4:
        .word   .LC0
.LC0:
        .ascii  "%d\012\000"

And

#include <stdio.h>
#include <stdlib.h>

int my_abs(int x)
{
    return x < 0 ? -x : x;
}

int main(void)
{
    srand(111);
    int x = rand() - 200;
    printf("%d\n", my_abs(x));
}

results in

my_abs:
        cmp     r0, #0
        rsblt   r0, r0, #0
        bx      lr
main:
        push    {r4, lr}
        mov     r0, #111
        bl      srand
        bl      rand
        sub     r1, r0, #200
        cmp     r1, #0
        rsblt   r1, r1, #0
        ldr     r0, .L5
        bl      printf
        mov     r0, #0
        pop     {r4, pc}
.L5:
        .word   .LC0
.LC0:
        .ascii  "%d\012\000"

Notice that the main code is identical (only a label name is different) in both programs as my_abs got inlined, and its implementation is the same as the standard one.

I think you can probably figure this one out just with a hint.

What happens to negative numbers when they are multiplied by -1?

Note that you can check if numbers are less than zero using if and then do something about less than zero numbers.

If you still get stuck after thinking on that for a few minutes shoot me a pm.

Edit: as long as you don't ask me to just write out all the code for you.