I don't think there's a word in English that means between 10 and 20. You might as well say "somewhere between 10 and 20", or, if that's too long, you might try "15, give or take."
One set of terms that has come into vogue relatively recently includes words like thirtysomething or fortysomething, which were initially used to describe a person's age, but I suppose those words could be borrowed to describe an amount as well, such as, "We caught twentysomething fish last weekend." However, this would be considered an informal and unconventional use of such terms; when such words are included in the dictionary, there is often explicit mention of age.
At least in the U.S., the term thirtysomething entered the mainstream vernacular along with a hit television series by the same name. Used conversationally, I don't think many people would bat an eye when hearing such words, but the words are far from officially established.
So, I wondered if one might use "tensomething" to go along with twentysomething, thirtysomething, etc. However, there don't seem to be any instances of that word in published works. When I Googled "tensomething," the first tensomething hits were twitter handles and message board names, but, sifting through those results further, I did manage to find a few uses of the word, mostly by bloggers who were referring to someone of that age, like these:
I love the spice girls, they totally rocked my world when I was tensomething.
There he was, this geeky, gawky little tensomething wandering dazed and confused around his native North Carolina, with half his head full of Boz Scaggs and Eric Carmen...
although I did find one person who used the word in the sense you are looking for:
This has happened to meh liek tensomething tiems. [sic]
So, if you want to follow the lead of one careless typist, you have your precedent. Use tensomething. However, don't expect much support from the dictionaries at this time.