English number words are pretty logical after a point. From twenty-one to ninety-nine, the same principle applies: you say the tens place followed by the units place. But the teens are different. Not only does the ten (which is where the word teen comes from) come after the units place (10+7 is not teen-seven but seventeen), eleven and twelve don't fit in at all.
Eleven and twelve come from the Old English words endleofan and twelf, which can be traced back further to a time when they were ain+lif and twa+lif. So what did this –lif mean? The best guess etymologists have is that it is from a root for "to leave." Ainlif is "one left (after ten)" and twalif is "two left (after ten)."