If you've recently installed Windows 10 and you're unable to launch any CC apps because you're getting the message that you've used both activations, you may need to change your login account to a local login if you're logged in with your Microsoft account.
Before upgrading to Windows 10 on Tuesday I made sure to log out of my CC account so I wouldn't have any issues when reinstalling. Did the upgrade to Windows 10 and selected the option of not keeping anything, and then installed CC and a few apps. Launched an app and found that I received a message that I was already activated on two computers. I attempted the option to deactivate on all the other computers but that failed as well so I did a chat with tech support.
We went through a lot of steps and found that on my other computer I could log out of the account and then try to launch the app on this computer but it still didn't log in. I then tried my personal login account, as I was trying to use my work login, and that account didn't work either. As I've only ever used my personal login on one computer there was no reason why it would also have a login problem.
I wanted to see if the problem was possibly something that's already screwed up in the login account, which is set as as an admin account already, so I wanted to just create a new account and log in with that one. When I setup the computer I opted to just use my Microsoft account due to being unable to use OneDrive when you're using a local or domain account, but when you're logged into Windows 10 with a Microsoft account you really only have the option of setting up the computer with another Microsoft account. You can opt to setup a brand new account which is then given an outlook.com e-mail address, but I didn't want to go through that hassle, so I just changed my login to a local account.
This is what ultimately solved the problem. I'm not sure what's going on with the Microsoft accounts in Windows 10, but it was preventing Adobe CC from communicating with with activation servers properly. The weird thing is that it wasn't that the communication with the activation server was just not functioning, but Adobe CC was reporting that both activations were taken. It's possible that there was really another issue but that the CC desktop app doesn't know how to report to the end user what the issue is.
On the bright side the issue has been resolved so I'm passing on this information to anyone else who may be having the same problem.