Is a 10 gallon tank big enough for an adult bearded dragon?

No, it isn't. Bearded Dragon's grow to 16-24" and a 10 gallon tank does not have enough room for food, water a log and it to move around. A 40 gallon tank is the minimum. If you cannot afford one new, check on Craigslist.org for a used one. You will need a screen top to put the basking light, heat light and UVB light on.