If the number is odd,
can only be 1, 3, 5, 7 or 9.
If the number is less than 30,
can be 1 or 2.
The sum of the digits has to be 10, so
can't be 2, because it would lead to the number 28, which is even.
So,
has to be 1, which implies that

In fact, the number 19:
- is odd
- the unit digit is greater than the tens digit (
) - is less than 30
- the sum of its digits is 10