Take a look at the video posted by dailylivin on this thread. If your tang the same white spots, then your fish AND your tank now both have Marine Ich (Cryptocryon irritans). You have to treat both fish and tank.
1. Fish treatment. You have to take the fish out of the main tank and into a quarantine/hospital tank. Do not be tempted to leave him alone because he is eating. The spots can disappear, but all it means is that the Ich cycle is simply progressing. It does not mean it or the tank is cured. Your best chance of curing the disease is one of 3 methods: hyposalinity, tank transfer, or copper. You can easily look these up. Nothing else consistently works.
2. Tank treatment. The tank has to stay fishless for at least 6 weeks, preferably 8. Without fish, the Ich parasite will die off in that period.
The Ich parasite is a curse in saltwater aquariums. Some people choose to live with it and take the risk of fish death and some do alright, some people do not want to risk it and so QT and treat all fish. It's up to you. I suggest you treat, especially if you want to put more tangs in your tank, like the hippo.