You don't need to own the Windows 10 media.
You just need a correct windows key that are associated to that computer.
You just download the windows 10 ISO file and burn that to some USB Drive.
Then you can boot from that USB Drive and reformat your SSD and reinstall windows from scratch.
What you
loose is some specific drivers that are associated with your computer.
You have to download this from your computer manufacture.
Some computers also have a specific partition on the SSD to make a hole fabric recovery of the operating system. You have to read how to boot to that recovery option.
But if you don't have that you need to download some drivers.
It very easy if you download the iso file from linux and burn the iso from windows with program like rufus.
Just go the the link with a webbrowser in linux to:
https://www.microsoft.com/software-download/windows10ISOIf you go to this link with a windows webbrowser you will be redirected to another link.
You can avoid that with some tricks in Chrome, like hold down <CTRL><SHIFT><I> to enable Tools for Programmer, and then hold down. <CRTL><SHIFT><M> to enable Mobile Mode. And then just reload that page you will not be redirected any more.