The instructions for updating Adobe's Brackets editor, while simple, haven't yet published in an easily-Googled location.
- Download the latest Brackets package for your platform
- Close all open instances of Brackets
- Run the update command:
sudo dpkg --install Brackets-package-name.deb
- Reopen Brackets
Note that this only applies to distros that accept the debian package. If you don't take debians, you'll have to build it from source.