I'm running a 10 gallon tank (I know it's too small) and I currently have 2 Black Skirt Tetras in it. (That's all).

Anyways one of the tetras is very social and active and commonly stays in the middle of the tank and just swims around. The other tetra is a little bit smaller and commonly finds a quiet place to hide and will just sit there for hours.

I haven't been able to accurately sex them to a point where I'm convinced but I think I may have one male and one female, the male being the shy one. Now these are my first two fish and I understand black tetras can be a little feisty, the larger one seems to bully the smaller one a bit. I'm not sure if this is normal behavior? When the smaller one does come out they both swim along together sometimes and the rest of the time the bigger one scares it back to its corner. Is this just a hierarchy forming in my tank? I know black tetras are best in small schools so I'm wondering what a good number is for a 10 gallon tank to make sure they're secure/happy until I can upgrade my tank size to something more appropriate for this species.

Also- I'm going away for 10 days, what's the best way to take care of the fish? I was going to do a 25% water change before I left and drop in one of those 14 days of food tablets, anything else I should do?

One of the reasons you are always advised to keep shoaling fish in groups is because there will be a dominance heirarchy, and the more dominant fish spread their inate aggression out amongst the group. If there is only one other, (or very small number), s/he will get all of it. TYpically in such a situation, the more dominant will hound the subordinate to death.

Another reason for keeping a group is that shoaling fish feel secure in groups. When insecure, they are carrying a greater or smaller stress loading. This stress can manifest itself in various ways. Some fish just hide, fade away and eventually die. Others become out and out terrors and attack anything that moves. There is a continuous spectrum of middle ground possibilities.

These are two of your problems and the solution to both is to increase your group size. You want probably 6 or more of that species. Now your third problem comes into play, your tank is not really big enough to hold a decent sized group of much at all. You can certainly add more now, but really, at full size they will overstock your tank somewhat. There will, of course, not be room for anything else. I am assuming of course that your tank is fully cycled and that your stats are 0 ammonia and nitrite.

As for going away, if I am away for up to 14 days, I do nothing. The fish are well capable of looking after themselves for such a period. That said, my tanks are large, mature and very low stocked.

I wouldn't add those white block things, they dissolve, and all that stuff is going into your water. If you don't think there is enough natural food production in your tank to keep your fish from starving, (could be the case with a small tank), then I'd try to arrange for someone to drop a feed in half way through. Hide your food. Measure out a normal sized dose and give the person a date to feed on. If you leave the food around, inexpert hands tend to overfeed, often hugely, without the expertise to sort out the resulting pollution spikes.