Hi
Sorry to hear about your poorly fish
I think the best thing to do is to try and figure out why the sickly one isn't eating - there must be a reason for it, and unless there is actual bullying from the healthy one I'm not sure theres any point in separating them.
So, if you could answer a couple of questions it would really help...
Do you have a test kit to test the water, and if so can you tell us results for ammonia, nitrite & nitrate?
When you say that the tank is 'big' - how big do you mean? If you don't know it in litres or gallons then just the tank dimensions will do.
How long has the tank been set up and was it cycled before the fish were added?
Is there a filter in the tank and what kind is it?
Lastly is there any chance of getting a pic of them up? I'm not too sure what you mean by them being golfish-types but not actually goldfish... maybe they're fancy goldfish? Anyway, it'll help if we can identify exactly what they are!
Sorry for all the questions, but the more information you can give the easier it'll be to figure out whats gone wrong