I have had an interesting experience with loneliness. The school system in which I enrolled during all of middle and high school (six school years, right now I'm waiting to start college in a couple of weeks) starts classes in the first week of August and ends in April (usually in the first week, sometimes in the second). The whole school year is tightly packed. Each individual school subject has to be taught at a steady pace, perhaps strenuous when compared to other school systems. Teachers may allow students to completely skip the final exam if they did well throughout the school year.
When not on vacations, I do feel quite pressured to be more commandeering, direct and active than I would naturally like to be. School days are absolutely EXHAUSTING to me for that reason alone, but giving in has served me well. I have been elected class president several times, teachers in general take me somewhat more seriously than they take many of my classmates, and so on. If I don't put on that "mask", teachers won't pay too much attention to me -- and the system I was in allows teachers to extremely strongly favor students whom they like -- it's very unstandardized, but it comes out being more interesting. (I'm usually on good terms with all my teachers, but maybe if I got the short end of the stick I would say it's boring and useless, who knows.)
When I get home, I'm beaten to a pulp. I have no desire to speak to my family. I feel drained, tired. I go in my room, work out, take care of any homework that needs being taken care of, read, and go to bed. It is not on many days that I have the energy to sustain significant conversations in the afternoon after school is over. I usually don't pay much attention to Facebook, though I have it open in the background in case anything shows up. I am quite OK with my afternoons being like that. I know I'm alone, but I don't mind; school is more than enough non-aloneness for me.
My mother (who is more or less the only person I'm with outside of school when in non-solitude) does understand that I'm tired, but she doesn't understand why. She's very active, outgoing and effervescent, being around people gets her going. She often hints that I should go out more/ try to find a girlfriend/ invite some friends to come over/ try going to a party. When and if I do try, things tend to not go well. People tend to like me, but I don't particularly like most people. >__>
(I remember reading an article that said INTPs have the highest divorce rate of all types, or something along those lines. People like us, but we don't like them as much.)
I had some golden luck in my last year: I found an ISTJ-ish friend who was willing to listen to me (listening to what I really wanted to say) and I was willing to listen to him. He's very calm, relaxed, geeky and curious. We'd sit together in class and discuss physics, metaphysics, economics, ways to improve our school, whatever was on our minds. He's quite smart (school-smart, if that makes any sense) so neither of us had problems at all.
My average grades across all classes hover around a 90-92, so most teachers do often allow me to forgo final exams. I am then left with the better part of four months' worth of summer vacations, which I spend reading twelve to fourteen hours a day. It feels odd after the first couple of weeks, but I very much enjoy the change of pace: books, my computer, tea, tobacco, and I. I'll talk with my family plenty more as well, if they have the energy to do so, even if they get home late from work. After the four months are over, I still don't feel very compelled to be around others, but I realize school is more fruitful for me if I bite the bullet.
I like to be alone. It's tiring to not be alone, save very few people. I deliberately use my "extroversion battery" in school because I consider it more efficient to do so.
EDIT: English is not my first language. Some of these things I just wrote did sound funny in my head; sorry for any inaccuracies.