No. You can never solo them. Once you can, you get 6xp. And this is something very annoying in fact. Being premium I've got easier leveling BUT.
If I'm 28 on Nar Shadaa and I can do Heroic 2+ with just my companion, then why the hell I get only 6xp for that? This is something really not refined enough. On one hand you can level higher, on the other heroic mission start to be something not very profitable.
And MMO or not, people can have a choice if they want to solo or group. I guess the way it is right now would be quite fair if only xp was counted fairly. Even with much higher level, if you'd get just the experience that was meant for the mission, no one would get hurt. Imagine level 32 getting xp for Tython's heroic. How much it was there? 500? 1000? What does it mean for a level 32 who needs dozens of thousand to get anyway?
Oh, and by the way: the same goes for my combat missions. Some of them don't appear anymore (e.g. the first mission was probably Fondor Escort and I don't get it anymore), while the other keep returning on the terminal. I keep getting a mission for level 18 and when I do it, I get 6 xp in return. So why the hell it keeps appearing if it's not for my level?