Let the numbers be xy = a
Then the reverse number will be yx = b.
Given the sum of the digits = 7
==> x + y = 7
==> y= 7-x.............(1).
==> b-a = 9
==> (7-x)x - x(7-x) = 9
==> (7-x)*10 + x = b
==> 70-10x...
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Let the numbers be xy = a
Then the reverse number will be yx = b.
Given the sum of the digits = 7
==> x + y = 7
==> y= 7-x.............(1).
==> b-a = 9
==> (7-x)x - x(7-x) = 9
==> (7-x)*10 + x = b
==> 70-10x + x = b
==> 70-9x = b...........(1)
==> x*10+ (7-x) = b.
But b-a = 9 ==> a= b-9
==> x*10+ (7-x) = b-9
==> 10x + 7 - x + 9 = b
==> 9x + 16 = b..............(2)
We will add (1) and (2).
==> 86 = 2b
==> b= 43
==> a= 34
==> Then, the two digit number is 34.
To check:
3+ 4 = 7
Also, 43 - 34 = 9