First we have to pick the tens digits as large as possible.
So we know that one of the tens digits is 9 and since no digit
appears more than once, the other tens digit has to be 8 
The two ones digits have to be as large as possible and they can't
be 8 or 9, so they have to be 7 and 6, so we could have either of these:


X + Y = 86 + 97 = 183
X + Y = 87 + 96 = 183


[They didn't, but if they had asked for the smallest instead of the largest,
the answer would have been either of these

X + Y = 10 + 23 = 33
X + Y = 13 + 20 = 33

Edwin