Welcome to Tropical Fish Keeping forum, palnud and variety.
Now for the not-so-good news: you are both likely heading for trouble with your Black Widow Tetra. BTW, this fish like many others has a lot of "common" names, but the scientific name is Gymnocorymbus ternetzi and using this will ensure you are talking about the same fish. And you will note that the names shaded, which means this fish is in the profile under these names, so you can click the shaded name for a link to the profile.
This fish, like all tetra, is a shoaling fish. That means, it lives in large groups of hundreds, and being in a group is an essential part of the fish's requirements. Most suggest six as the minimum number for a tetra species, but more is always better. However, tank space has to be considered, and as someone mentioned, a 10g is very limited space. This fish should be in a 2-foot tank (a 15g or 20g) minimum, and in a group of more than six.
Now, the reasons. Shoaling fish have a need for numbers as security; the more there are, the safer they will be. And that means less stress, and stress is the main cause of all fish disease. Second, there may be a hierarchy within the group, natural to the fish; interactions between males, a pecking order, etc is a part of the fish's needs. When denied this, fish can react in various ways, but the most common is aggression. The fish is simply frustrated at not being in an environment that nature programmed into it, and it lashes out the only way it can. Other times, the opposite may occur; the fish becomes withdrawn. In both cases, stress again results, leading to health problems. Some of these cannot be seen until it is too late; when fish die earlier than their normal lifespan, it is almost always due to some facet of stress caused by an inappropriate environment.
I can't advise what to do, but in both cases you should have more of this species, and in sufficient space, if you want the fish to be at its best. Among tetra, this species is known as a bit of a fin nipper when it is not properly maintained, so you can expect this to break at some point.