Cannot install brew on Mojave with Xcode 10

After installing CLT, you can ask CLT to add header files to /usr/include, then homebrew will appropriate detect the Command Line Tools.

installer -pkg /Library/Developer/CommandLineTools/Packages/macOS_SDK_headers_for_macOS_10.14.pkg -target /

Beginning in 10.14, a new step is required to create the header files in /usr/include:

Install /Library/Developer/CommandLineTools/Packages/macOS_SDK_headers_for_macOS_10.14.pkg

Source: The Xcode 10 release notes

You will need to install both "Xcode 10.0 Beta" from https://developer.apple.com/download/ AND "Command Line Tools (macOS 10.14) for Xcode 10 Beta" from

https://download.developer.apple.com/Developer_Tools/Command_Line_Tools_macOS_10.14_for_Xcode_10/Command_Line_Tools_macOS_10.14_for_Xcode_10.dmg

Update contributed by other comments, after you installed "Command Line Tools", you will also need to execute the following command in your terminal.

open /Library/Developer/CommandLineTools/Packages/macOS_SDK_headers_for_macOS_10.14.pkg