The first number must end in 9 (the sum of the digits must be even, adding 1 to generate the next number must generate a carry to keep the sum even). 99 is balanced, but does not work since the following number, 100 is not balanced. We then try to find the smallest three-digit number ending in 9 such that the first two digits sum to 9. We know that the second number will have a zero in the one's place with a carry generated. The remaining two digits would have summed to 9 without the carry, so must sum to 10 with the carry. Since there is a zero in the one's place, the two remaing digits must be equal, so the second number must be 550 and the first must be 549.