You can actually have creative cloud installed and signed in on two computers, as long as you only use it on one at a time. Download and install as you did on the first computer, sign in to your Adobe account on the Adobe website using your Adobe ID, download the Cloud desktop app, then download the software. Sign out on a computer that you will not be using: sign in and sign out of the Adobe Creative Cloud desktop app
You can download the installer for Creative Cloud from here :
Creative Cloud Help | Creative Cloud for desktop.
After you install the Creative Cloud desktop application , you will need to sign in with an Adobe ID and Password. Then you can install apps. This link offers more information and step by step instructions if you need it: Creative Cloud Help | Download, install, update, or uninstall apps
A CC subscription can be used for either platform (or both since you are allowed to have two activated installations)