How do I replace one of my two Macs?

excellent question that's going to save you a lot of aggravation and time.

******************* beginning of answer to your question *****************

simply install the cc desktop app on your new mac and sign in with your adobe id and password.  use the cc desktop app from here https://creativecloud.adobe.com/apps/all/desktop?action=install&source=apps&productId=creative-cloud to install your adobe subscription and trial programs.

if you have trouble downloading, use the alternative download site at page bottom here, https://helpx.adobe.com/in/download-install/kb/creative-cloud-desktop-app-download.html

**************** end of answer to your question ****************

*************** beginning of answer to a different (migration) question ************

do not use time machine or any other migration tool to move your adobe programs from one computer to another.  if you are going to use a migration tool:

on your old computer

1. uninstall every cc app including preferences, https://helpx.adobe.com/creative-cloud/help/uninstall-remove-app.html

2. uninstall the cc desktop app, using the correct uninstaller, https://helpx.adobe.com/creative-cloud/help/uninstall-creative-cloud-desktop-app.html#sa_src=web-messaging

3. clean your computer of cc files per http://www.adobe.com/support/contact/cscleanertool.html

4. use your migration tool to migrate your old (adobe-free) computer to your new computer.

on your new computuer

1. install the cc desktop app

2.  sign in to the app

3.  use the app to install your adobe programs

************** end of answer to a different (migration) question ***********