I think I've found one that I can put in here. While I listen to all kinds of music when wanting solitude, I do tend to listen to ones I can sort of recognize myself in. There is something about the "right" music being able to make even the saddest messages beautiful in its own, special way.
I seldom really wish for solitude, but often it is the only alternative to what I want to escape from. If things were ideal I'd have a friend I could run to who would not "just" be there for me but also be capable of understanding me.
Anyways, one of the more recurring artists in my music library is Sia Furler. I often find that her live performances sound so much better than the studio albums, so I'll embed a live (on radio) one for you.
Lyrics for the specially interested.

Help, I have done it again
I have been here many times before
Hurt myself again today
And, the worst part is there's no-one else to blame
Be my friend
Hold me, wrap me up
Unfold me
I am small
I'm needy
Warm me up
And breathe me
Ouch I have lost myself again
Lost myself and I am nowhere to be found,
Yeah I think that I might break
I've lost myself again and I feel unsafe
Be my friend
Hold me, wrap me up
Unfold me
I am small
I'm needy
Warm me up
And breathe me
Be my friend
Hold me, wrap me up
Unfold me
I am small
I'm needy
Warm me up
And breathe me