I'd think that the most common type to be extroverted-loner would be ENFP. The balance of Ne (out of this world-thought process that doesn't really let you configure to society), and the Fi dynamic that kind of turns you against conformity and social ideals.
I am a total loner. I spend a lot of time alone and I don't think I have but a few close friends. I don't like it..to be honest..I'm just..different..? When I find people who get me, I make strong and deep bonds.
Perhaps being an extroverted loner has something to do with Enneagram. I am a strong 4, and I've known that to be kind of at the root of this dilemma.