Show that one can find 50 distinct positive integers such that the sum of each number and its digits is the same.

If I understand the problem correctly, we are looking for sets of numbers that when each is added to its individual digits, a number

results that is the same number for all members of the set. For example, consider the pair: 92 and 101. Or consider the pair: 9900035 and 9899999.

I am thinking such numbers come in pairs only.