We can start with:
x + y = N
where
x is the first 3 digit number
y is the second 3 digit number
In order to get the maximum value of N, the digits used must 9,8,7,6,5,4
To maximize, 9 and 8 must be added. This can only happen if 9 is the first digit of the first number and 8 is the first digit of the second number. The same idea is applied to the other digits. So
x must be 975 and
y must be 864
N = 975 + 864 = 1839
