Most suggest a 20 gal tank and as up to a 30 and all you need is a good skimmer to manage this tank with just some reg type of lighting and piping for hiding places with a small heater for when treating any ill fish, you need to keep the tank a bit warmer near like 83F But being you would have a HOB skimmer and when you need to apply any medications the skimmer would have to be lowered down some on the air intake for it would remove the medicine real quick like.
Now I on this of a QT, im using a 40 gal tank for when the reef tanks are ready to begin stocking and I a dusting of aragonite sand for which is not even a 1/4" for a deep sand bed when treating with copper, it will linger in the tank a long time.
Now if you are thin king about setting it up right away and placing this eel in it, you will only finish it off in a hurry for even that you use water from this tank the eel is in, the tank will still have a cycle as well and this was already said, I wouldn't look to try and move this eel, but too get a good look at it and look to what you can do for it. If anything, remove the other fish.
For im concern here on a number of things for your eel, its stunt growth for one and is very unhealthy as well other pointers that were giving about the skimmer. I am sorry fella, for this eel and your disappointment for if the worst do happens here