Both are invitations to talk, but here's how I see the difference: Talk to me = you have something to tell me. Talk with me = lets discuss something, I want to hear you talk and I also have things to say.

There is not much difference, but just a little difference in emphasis. When you say "talk to me" you are emphasizing just having a communication with a person without regard to a particular subject. When you say "talk with me" there is an inference that there is a particular subject in mind to talk about.

Talk to me - "I want to hear what you have to say to me. Please tell me." Talk with me - There is some issue or feeling between the two people that they will talk about together. (or) Maybe the person who said this needs some company or comforting...

Next time, you might write a complete sentence that includes the phrase. That would be helpful. ^^