My landlord handed me an eviction notice, giving me 10 days to vacate the premise. This is because the basement flooded, and he is blaming the problem on me. Can he do this? Is he allowed to only give me 10 days?
No, he is not allowed to only give you 10 days to vacate.
If you have a lease, re-read it and see if there is something in there that gives him that right.
Let him take the next step and file an eviction in court and then you tell the Judge you did not receive proper notice of termination.