In the first example, you can choose, for example,a = 17 andb = 18, so thatS(17) + S(18) = 1 + 7 + 1 + 8 = 17. It can be shown that it is impossible to get a larger answer.
In the second test example, you can choose, for example,a = 500000001 andb = 499999999, withS(500000001) + S(499999999) = 82. It can be shown that it is impossible to get a larger answer.