Time Machine generally backs up everything in your user account, whether local copies of iCloud documents or other documents you may have locally.
If you have another copy of the document on your USB stick you might want to give that copy a try.
Another possibility worth a try: Make a copy of the document that you can't open as a backup. Then in Finder try changing the .numbers extension to something else and then back to .numbers again.
And also this might help: in Launchpad hold down the option key until the icons shake and click the x by the Numbers version with the four columns to uninstall it. Then download Numbers again from the Mac App Store.
SG