Error in Windows 10 setup: "Something happened"

I downloaded the Microsoft Media Creation Tool to create an ISO file for Windows 10. After selecting the version I want and clicking Next I got:

I can click Close and the program finishes without doing anything.

In a similar question the second text at least gives some more details.

In the diagerr.xml I can see the following error:

CSetupPlatform::ResurrectNewSystem: 
Failure: Win32Exception: \\?\C:\$Windows.~BT\Sources\NewSystem.dat: 
The system cannot find the file specified. [0x00000002] __cdecl    
UnBCL::FileStream::FileStream(const class UnBCL::String *,enum 
UnBCL::FileMode,enum UnBCL::FileAccess,enum UnBCL::FileShare,unsigned long)

Maybe the fact that the version of Windows I'm doing this on does not match the one I want to download has something to do with it?

Instead of using the Download Tool, you can access ISO images directly. Because Microsoft tries to force Windows users to use the Download Tool, you’ll have to change your browser’s user agent to something different, like this:

Mozilla/5.0 (Macintosh; Intel Mac OS X 10.10; rv:39.0) Gecko/20100101 Firefox/39.0

Then, go to the download page and select the appropriate ISO. It will contain both Home and Pro.

Be careful about the first selection (Plain/N/KN etc). It absolutely has to match your current installation, or upgrading will not be possible. If you’re only interested in a clean installation, it’s not really important.