What does the constant E do in the c language

The documentation for floating-point constants is here.

The form 1e2 or 1E2 means 1 times ten to the power of 2, and you're perfectly correct that 2E-1 means 2 times ten to the power of -1, or 0.2.

It's based on the scientific E notation linked by Eugene.

When I run the code it prints a weird number

That's just because you used the wrong format specifier. These are documented here, and you can see you should use one of eEfFgG for doubles.

From the 2018 C standard, clause 6.4.4.2, reworded:

• “A floating constant has a significand part that may be followed by an exponent part and a suffix that specifies its type.”
• The significand is a sequence of digits that may include a period. It represents a number in the usual way. For example, 3.4 represents 3 ones and 4 tenths.
• The exponent part is an e or E followed by an optional sign and a sequence of digits, such as e13 or e-4.
• The “exponent indicates the power of 10 by which the significand part is to be scaled.”
• “An unsuffixed floating constant has type double. If suffixed by the letter f or F, it has type float. If suffixed by the letter l or L, it has type long double.”

Thus 6.8558e-4f represents 6.8558•10⁻⁴ and produces a float value.

Note that most C implementations use a float format based on powers of 2, not 10, so they cannot represent 6.8558•10⁻⁴ exactly. In the format commonly used, IEEE-754 binary32, the closest representable value is 0.0006855800165794789791107177734375.

E notation

Most calculators and many computer programs present very large and very small results in scientific notation. Because superscripted exponents like 10⁷ cannot always be conveniently displayed, the letter E or e is often used to represent times ten raised to the power of (which would be written as "x 10^b") and is followed by the value of the exponent. Note that in this usage the character e is not related to the mathematical constant e or the exponential function e^x (a confusion that is less likely with capital E); and though it stands for exponent, the notation is usually referred to as (scientific) E notation or (scientific) e notation, rather than (scientific) exponential notation (though the latter also occurs). The use of this notation is not encouraged by publications.

As for your second question:

can we use this approach in other data type or we can only use it in floating points?

See the C# spec:

Real literals [the type of numeric literals that are allowed an E in them] are used to write values of types float, double, and decimal.

However, you have to cast or suffix the literal appropriately when assigning to anyhting other than a Double, because any literal with an e or E in it is recognized as a Double in Visual Studio. I cannot find where this behavior is specified.

float f1 = 7E1;     // Compile error. Needs F suffix (7E1F)
decimal d1 = 8E2;   // Compile error. Needs M suffix (8E2M)
double d2 = 9E3;    // Works.

int overninethousand = (int)9E3 + 1; // Works

float var = 1.54334E-34;
double var2 = 1.54334E-34;

printf("\n normal:%f\n sci:%e \n or \n sci:%E   \n",var,var,var);
printf("\n normal:%f\n sci:%e \n or \n sci:%E   \n",var2,var2* 1.0E3 ,var2 * 1.0e3);

According to Wikipedia:

In normalized scientific notation, the exponent b is chosen so that the absolute value of a remains at least one but less than ten (1 ≤ |a| < 10). Thus 350 is written as 3.5×10². This form allows easy comparison of numbers, as the exponent b gives the number's order of magnitude. In normalized notation, the exponent b is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as 5×10⁻¹). The 10 and exponent are often omitted when the exponent is 0.

Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalised form, such as engineering notation, is desired. Normalized scientific notation is often called exponential notation—although the latter term is more general and also applies when a is not restricted to the range 1 to 10 (as in engineering notation for instance) and to bases other than 10 (as in 3.15× 2²⁰).

That is 1e6, not le6, and it means 1 * 10^6 or 1000000.0

It is scientific notation.