Black Ich is different than White Spot Ich. The good news is that its not as potentially deadly. The bad news is that its more difficult to get rid of in the tank. These are little flat worms that spend part of their life on your fish and part in your substrate. When its on your fish, you can do a freshwater dip and follow with Formalin treatments. Some will be in the sand though, so leaving your tank fallow is the only way to kill those off. Apparently they can survive there for months feeding off debris/detritus (unlike Ich that needs a fish host). I've heard to go fallow in your DT for three months while your fish are in QT (which is not very practical). Siphoning the gravel to keep waste off the bottom helps keep their "food" scarce and might grab a few in the process, but it won't get them all.
I've heard of fish being able to live with this, but it seems to be based more on luck than science.
If this Yellow Tang is in a 40g, you are likely to have health issues moving forward. They really need much larger tanks to thrive.