I'm only level 11 at the moment, but my EM/FA Brute absolutely rages solo. I barely rest in missions, since going into a fight with a near-full rage bar is usually much more important than going in with near-full health. Things just don't last long enough to hurt you against that kind of damage, provided you've slotted for a little accuracy in your attacks.
I struggle to imagine a more soloable toon than my current one. Over the first 11 levels, anyway.