Each program is independent so, yes, you can certainly have them both on the same computer with no problem.
In fact, you should also be able to run Premiere Elements 1 and Premiere Elements 10 on the same computer with no problems.
Premiere Elements 10 and Premiere Pro CC are standalone programs.
Although I have not tried it first hand, I am almost sure that you can install both on the same computer and use one at a time. But, you can do better than my speculation, you can download and install the Premiere Pro CC tryout and determine how it performs in your computer environment.
Based on Supported Import Formats, I am not seeing you opening a Premiere Pro CC project file in Premiere Elements 10 Windows.
And, I have doubts about opening a Premiere Elements 10 Windows project file (.prel) in Premiere Pro CC Windows. According to the Premiere Pro CC Supported Import Formats, this is possible. But, a current thread suggests otherwise.
Please review the Premiere Elements 10 ReadMe
Thanks for the prompt replies. Only reason I am asking is because of my previous experience, upgrading from PE 1 to PE 10. This was on an earlier Windows PC I had, running Windows XP, but I don't want to repeat that experience. After installing PE 10 I found that my PC wasn't quite powerful enough to effectively run it, but after that I was never able to get PE 1 to open again. I tried everything - deleting PE 10 from my system, reinstalling PE 1, Windows system restore to an earlier date, etc, etc - and nothing worked. Eventually bought my new more powerful PC and installed PE 10, and everything has worked great since then.
At the moment I still have some open projects in PE 10, so I was concerned about being to open them in PE 10 after installing PP CC. Thanks for the links A.T. - I had already seen those posts about some users not being able to open PE 10 projects in PPCC.
Thanks for the reply.
I do not expect you to lose Premiere Elements 10 function by installing Premiere Elements 10 and Premiere Pro CC on the same Windows computer. Just use one program at a time.
My major concern with Premiere Elements 10 is it running on a computer with a NVIDIA GeForce video card/graphics card.
That is bad news where rolling back the driver version to May 2013 is the answer if you can find the NVIDIA GeForce driver old enough for your particular computer operating system.
If you do try to open Premiere Elements 10 project in Premiere Pro CC, please consider working from a copy of the Premiere Elements 10 project file (as a safety net).
As your schedule permits, please let us know the outcome. I do not think you will need them, but nonetheless just give yourself any many safety nets as possible.