MattM's right on the dot - turbellarian worms - a type of external parasite. In and of itself, they won't kill your tang, although your fish will probably "flash" and appear stressed.
Some tips on treatment...
DON'T treat your tank water with any medication/freshwater dip your fish. Generally speaking, this'll do more harm than good, esp in the case of a typically non-fatal parasitic infection.
DO consider adding a cleaner shrimp ie ("scarlet" or "skunk" cleaners) to your tank. If your tang's conducive, and most fish suffering from turbellarian worms are, a cleaner shrimp can alleviate this problem by picking the parasites from the fish's body. Also a good on-going preventative measure.
Also along preventative measure lines...
If you don't quarantine, the next time you purchase a fish, after acclimating it to your system, at least make sure you empty as little (ideally none) of the water from the store bag into your tank as possible. If you include this water, you're essentially sharing any free-swimming potentially harmful organisms remaining from any number of infested fish residing there previously. I'd empty all of that water into a separate bin prior to releasing any fish into your aquarium.
Good luck w/your tang.
