I am not from Laminar Research; just a flight simmer from downunder.
You haven't stated why you need to redownload. Why do you need to stay with XP10 when XP11 is far superior?
Without knowing when you purchased XP10 I presume the demo version was available then. This would have been a simple method of obtaining a second copy. But that version to the best of my knowledge is no longer available because XP11 is now the official version. So any replacement will be at a cost
If you want to reinstate the XP10 version you should deal directly with Laminar Research at email@example.com as this forum is not the place to make such a request.
Forget XP10 and update to X-Plane 11.