Turns out java has been moved into brew core recently, so the correct command as of August 2022 is:

brew install java

Then check your installation by running

java -version

If the result does not looks like this:

openjdk 18.0.2 2022-07-19
OpenJDK Runtime Environment Homebrew (build 18.0.2+0)
OpenJDK 64-Bit Server VM Homebrew (build 18.0.2+0, mixed mode, sharing)

but like this:

The operation couldn’t be completed. Unable to locate a Java Runtime.
Please visit http://www.java.com for information on installing Java.

Then you also need to create a symlink for the system Java wrappers to find this JDK:

sudo ln -sfn /opt/homebrew/opt/openjdk/libexec/openjdk.jdk \
     /Library/Java/JavaVirtualMachines/openjdk.jdk

I tested this answer using a clean install of High Sierra 10.13.6. All updates from Apple were installed.

The downloads of the JDKs can be found at Java Downloads. I could not correctly view this site using Safari under High Sierra. Instead, I installed and used Firefox ESR (Extend Support Release). This link for Firefox download can be successfull viewed from Safari. The file I downloaded and installed was Firefox 115.16.1esr.dmg.

I tried JDK 23 by downloading and installing jdk-23_macos-x64_bin.dmg. This was not recognized by Java. Next, I tried JDK 21 by downloading and installing jdk-21_macos-x64_bin.dmg. This was recognized by Java.

Instructions for uninstalling a JDK can be found here. Personally, I just used the Finder to move the /Library/Java/JavaVirtualMachines/jdk-23.jdk folder to the Trash.

I tested by using the simple code given below. The code was stored in the file named Simple.java.

class Simple{  
    public static void main(String args[]){  
     System.out.println("Hello Java");  
    }  
}

Example of testing is given below.

dmas-Mac:Desktop dma$ javac Simple.java 
dmas-Mac:Desktop dma$ java Simple
Hello Java

BTW, I tested JDK 23 using macOS Monterey and did not encounter the problems that occurred with High Sierra.

In 2022, you can use just brew

brew install openjdk

and maybe you need to update PATH env:

export PATH="/usr/local/opt/openjdk/bin:$PATH"

…and for the future give a try to sdkman, is better than brew

curl -s "https://get.sdkman.io" | bash

then open a new shell and try list to see what you could install ;-)

sdk list java 

At time of writing you could use:

sdk install java 17.0.1-tem