Those two sentences mean the exact same thing in ordinary speech. "together" means "as a group" "with each other" means that each person in a group is performing an actions with every other member of the group. They could mean different things, but only in rare situations. "Everybody in the room was reciting lines from the movie we had just watched. With so many people talking together, it was hard to even think." Here, "talking with each other" would not work. The people are together, and are all talking as a group, but they are not talking to the other members of the group, so they are not talking "to each other." This is a little bit of an awkward sentence, though, and almost every time you actually see or hear "talking together" it will mean "talking to each other"

I agree with Mike, but I want to point out that "Xing with each other" and "Xing together" do not always have the same meaning. There are cases where they have the opposite meaning. It depends on the verb you use. For example: They are competing with each other. (= A is trying to defeat B, and B is trying to defeat A) They are competing together. (= A and B are on the same team!) As you can see, the meanings are very different. The same will happen for similar verbs such as fight, debate, or battle.