Molly, no one can predict what a cat will do or how it will react, but I can tell you I have had cats all my life and I just tossed them together. Maybe held one and let someone else hold the new cat, let them look at each other, then continue to hold, let them smell each other up, and put them down. Sure, there was a bit of hissing. But things have always worked out in a couple of days.
Four years ago I adopted two females on the same date and brought them home and tossed them together. It took about a week of hissing (one was very frightened and defensive) but they learned to live together just fine.
This past spring one of my females got kidney failure and died. I waited a bit and adopted a 3 year old male and did the room separation/gradual introduction thing. Let me tell you, it has been a disaster. I am kicking myself every day for not putting them together ASAP. He is now dominating the home and my original little female is hiding all day long. We are talking about 6 months of this. I've tried all the remedies, but if he sees her come out and walk around, he beats the daylights out of her. I am determined to make it work and I keep him closed up in a room during the night so she can roam freely in HER house.
Why do I keep him? Because I love him! He's a great cat. She is too, but she's never been super friendly.
All I can tell you is good luck. If I had to do it all over again I would NOT do the separation thing. I don't care what all the silly pet psychiatrists tell you. There are other people on this site who agree with me. You can also put the new cat in a carrier and put her in the room, let the other smell her and see her. The only thing I might be concerned with in your situation is this is an older, adult cat, and she may not want to play like the younger ones.