In the battle at the end of Brisingr, Eragon tells Murtagh that the solution to his problem is to change his True Name. That, by changing his True Name, Galbatorix can no longer keep hold of whatever magic that was cast on him and that he will be free. This was faintly alluded to the sentence he decided upon for Sloan.

Now, earlier in the books, Arya speaks of the war where Galbatorix and the Forsworn kill the other Dragonriders. During this story, she speaks of the Dragons of the Forsworn and why they are never mentioned by name. The story goes that when the treachery of the Dragons(and their Riders) was discovered, the other Dragons banded together and cast a spell over the Dragons. Over time the spell erased the True Name of the Dragons. Small details of their personalities vanished and over time they wet mad and eventually mindless. In addition, their Names vanished from memory. No one can say their names, even those that are written down. They can't be read. They can be copied, but only if you go one character at a time.

Now, a True Name consists of everything you are at present. However, they spell erased parts of their name. This means their Names have changed. If your name changes, any spell cast upon you using your True Name stops, because that person(as per their True Name) no longer exists. This means the second any part of the Forsworn Dragons True Names was erased, the spell should stop working.

Using your name as an example:

Let's say Aludra represents everything you are as a person. It represents your very existence. Using magic, I cast a spell to erase your Name. Let's say the first thing I erase the 'A'. This represents your love of Jim Butcher, and strawberry pop tarts and your love of the scent of freshly cut grass and how you defend the things you love with every weapon at your disposal. I've just erased all of that, and fundamentally changed you as a person. You are now Ludra, and the person known as Aludra no longer exists. The spell I originally cast, though, named Aludra as its target, but that person no longer exists, so that spell evaporates like it was never cast. This means your True Name is no longer being erased.

in one morning(roughly six hours), Eragon cures cancer(despite not knowing anything about the human body, or medicine, or how tumors work). He partially erases a powerful spell he put on Elva. Oh, and he also pulls millions of tiny individual atoms of gold out of the soil to give himself three large-sized spheres of pure gold. This doesn't wind him in the slightest, nor does he have to draw on any of the secret reservoirs of power he has.

On the other hand, again, in the battle at the end of Brisingr, thirteen Elves, some of them hundreds or thousands of years his senior, are utterly exhausted after healing one relatively minor wound to Saphira. And to forestall the argument, these are the best mages the Elves have to offer.