I found a discussion of Office 2013, keeping it, here:
https://answers.microsoft.com/en-us/msoffice/forum/all/reinstall-windows-10-but-keep-microsoft-office/d73df984-ef71-4bf2-8ee8-46941eb5db2f
It says basically the same thing, you need the original media and key and without that, you can't keep it once it's wiped. The only other option I can think of it to get a hack for the key, but that's not really a good option in my experience as often such hacks either don't work, or they might open you up to other problems. What I recommend is use Open Office instead. It's a very capable program and if you need to, you can open the files in Microsoft Office and save them there a second time in Microsoft's format. Do understand though that MS Office will not keep any fancy features you might use in OO in the transition. It's good enough to get started though, and sometimes that is all you need.