IMHO, I think both are probably starving do to lack of photosynthesis from a light fixture that isn't intense enough. I have a 40g cube and I have 250 watts of lighting for zoas and anemones... you have a smaller tank, but 16 watts just isn't even close. I have a 16g holding tank and even it has 160 watts. Sorry.
I think the nem is closer to dead than the tree coral. Beg, borrow or buy a new fixture of at least 100 watts and there is a slim chance for the nem and a slightly better chance for the coral. An Mars Aqua led fixture is only $100 and would be just what you need. It's got 55 3 watt leds driven at 1.85 watts which is 100 watts!