Windows 10 Setup has failed to validate the product key

I read through the log files in C:\$Windows.~BT and discovered an error message that said:

Unable to create temp file in C:\Users\me\AppData\Local\Temp. The file already exists.

(That's not the exact wording, but it's pretty close. I'm typing this on my other machine while watching the installer run.)

I ran Disk Cleanup on the drive, which cleared out the Temp folder and the downloaded/unpacked installer files (in C:\$Windows.~BT and C:\$Windows.~WS), then started the installer again and had no trouble.

None of the other answers worked for me, though Moshe Katz's answer did point me to the log files. Under C:\$Windows.~BT\Sources\Panther there are two log files, including an setuperr.log which indicated to me that it was in fact a license key issue. This did cause me a little confusion because I was never prompted to enter a key; I suspect Setup was attempting to autoactivate using the Windows 7 key or was looking for a Windows 10 OEM license in the BIOS.

I opened an admin command prompt, browsed to C:\ESD\ where the media creation tool stores its files, and I ran setup /pkey xxxxx-xxxxx-xxxxx-xxxxx-xxxxx using the retail product key we purchased and Setup worked perfectly.