数 in 十数 means that it is an unspecified number. That is, 十数 is 1X, where X is an unspecified digit. It is usually assumed that X is at least two and not too large; 19 would be probably too large to refer to as 十数.
This usage is not limited to 十数; the same usage can be seen in other unspecified numbers such as 数, 数十, 二十数, 三百数十, and so on. In most cases, using an unspecified number without a counter word would be incorrect or at least unnatural.
Although some people write 十数 as 10数, other people (including me) consider that the notation 10数 is wrong because recovering an actual digit (say, 3) in place of the letter 数 would make it something like 103, which is different from the intent.