If I had that problem, and couldn't find someone here to tell me authoritatively what's wrong, my guess would be that Excel 2013 works ok (as evidenced by the fact that it's opening documents just fine), but that Windows still has Excel 2010 in its associations. When you get Excel 2013 to open a file, you see, you know that Excel 2013 is doing it. When you double-click on an Excel document in Windows, Windows looks to see what app should open it. Sounds like maybe—this is just an hypothesis—that Windows is asking Excel 2010 to open it, and running into a problem.

But while I think I'm good inside Excel, I get kind of vague when I have to figure out how Excel is interacting with Windows. Don't believe my answer until someone else here agrees with me.