The latest Windows 10 update removed my Office licence. Once running any office program, it asks me to sign in with the associated account.
A pop up then appears with
"Sorry, we ran into a problem while trying to install the product key. If this keeps happening, you should try repairing your office product. (System error: 0xc06d007e)"
The update is "Update for Microsoft Windows (KB3176929)"
It's unlikely to have removed your key. Try running a quick and then online repair if that doesn't fix it. It just sounds like it's managed to confuse itself.
Was it an "official" Office license, or a grey market "official" Office license?
Like from kinguing or any of those cheap online sell platforms.
That was my initial thought as well, tried both and got nothing
Official, as provided by my university
Try running a key finder program like MagicJellyBean, or ProduKey?
What version of office are you running? example: 2013 Home and Business