From the picture of the barrel adjuster (the little knob on the brake lever), it looks like you could loosen the cable a bit using that.

There are two components to the barrel adjuster - the barrel and the lock ring. The lock ring is the black ring around the silver part. That is likely tightened down against the lever to keep the barrel from moving. You can unscrew that slightly with a little bit of force - you should be able to do it with your bare hand. Uncscrew it a couple of turns then screw the barrel into the lever body a couple of turns. This should make the brake feel a bit looser and give you the ability to more easily detach and reattach the brake.