Here's what I see....
Your dog was guarding his chew. I think that you need to work on resource guarding with him so that he knows you will take charge when someone else is in his space. this is something I deal with in my house. We have a resource guarder. You have to work on that individually so he doesn't feel the need to do that.
Second, I would say your foster reacted to the "aggression" as a threat and thought of it as self defense. Once again, you need to place yourself in a position in their eyes that you are in charge.
i would start using NILIF (Nothing In Life is Free) on both of them. You can do a google search and come up with much information.
Second, no chews/toys/treats unless both have and are supervised.
Third, I would NOT leave them alone together on the chance that something happens while you aren't there. We have two females here that we don't dare leave alone without crating one. 99.9% of the time they are great together. It's the 0.01% that we have to worry about.
I think what you have right now are two very nice dogs that are confused about their place in the house. You need to show them that both are safe, both are loved and that you will be the one to solve the problems. You really have to have good timing and be on top of things.
Just as an example, our oldest boxer (11 yrs old) was smelling Jax's bottom while she was laying on the ottoman at my feet. Jax curled her lip at her and gave a little growl. I was so amazed that Jax did that I just watched her. She did it again and Banshee continued to sniff her butt. She did it a third time and as I reached for her to stop her and tell Banshee to move back, she came off the ottoman and attacked. Lots of noise, no bloodshed, all happened in less than 90 seconds. That was 100% my fault because I didn't react to let her know I had it under control and would get Banshee out of her space.