Fin/Tail Rot?

Yesterday I got a new macoskers wrasse. Today when I came in half its tail was gone and it had what looked to be white specks around the area. I tried to catch the fish so I could put it in a ten gallon. During this time I spooked my solar wrasse and he hid for about a 45 minutes. When he reappeared he had white specks on his tail to and it looked like it was melting away. What could this be. I just did a water change and all is normal. Another thing is that it appears the specks come off the fishes tail every so often while it swims.

 

its really hard to tell from the pics. do you have other fish that would attack these? if i were you i would dose your tank with stress coat and soak some brine in garlic for feeding. I would also get a product called "Selcon" and feed with this additive. Is there any spots elswhere on the fish? Do you have a UV sterilizer? What all peramiters are you testing for? and what method of testing are you doing ie.. strips or test kit. Going to need a bit more info to be truly helpful.

 

One fish was new the other was the biggest fish in the tank.