I legitimately don't know what the problem-solving process would be like for Fe users. I know that I was talking to @fidelia a bit ago about how some NFJs will go through a similar "make this emotion go away" process with anger, as opposed to with sadness, but she didn't go into details.
Also @Lady X is right -- I hear a lot more of that sort of talk from my Fe family members and friends.
e.g. if you asked an Fe person I know about a traumatic event in their childhood, they'd be quick to attribute the blame. It would be all about who the blame went to. That would be how they coped with the event, would be attributing blame. Whereas if you asked me, or one of my Fi friends, it would be less about whose fault it was, and more about the fallout from the event -- how it made me feel, why it made me feel that way, how I looked within myself to see why it made me upset (and here might be where I attribute blame, but I wouldn't be considering blame to be the most important thing). There would be a deeper conclusion at the end, than "It was this event or this person, end of story"; more like "I couldn't tolerate that event because I reacted a particular way; some of it was because of the person or the event, but if the same thing had happened to me now, I may have reacted differently."
If I'm right, then I suppose you could phrase it like this: Lack of who/what/where/when/why information -- replaced by irrational Fe judgments and assumptions -- makes Ti stressed out, so Ti will try to create order out of chaos by contributing that information and providing closure that way. Whereas overwhelming, animalistic, value-based feeling, overwhelming your senses and your reason, is what stresses Te out, so Te will try to create order out of chaos by calming the feelings down, validating them so that they stay content and won't try to rise up again.
Everyone, let me know if I'm leading @greenfairy in the wrong direction here.