Whenever I was in this situation, I would put up two or three mesh baby gates, (the number depending on the door height), .....in the doorway of the room where I kept the newcomer. That way no one would jump the gate....and yet they could smell each other and hiss etc. and even touch, but couldn't hurt each other. Eventually the gates would come down. It usually took two weeks.

It has always worked for me. I have even done this arrangement at the bottom of a set of stairs.

Good luck.

I know how horrible it is to hear the hissing and howling. Been there, done that, and it ends at some point, honestly.