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Let the digit in units place be x
The digit in tens place should be 8-x (as sum of the digits is 8)

The number is 10(8-x)+x = 80-9x

If 8 is added to the number, the digits are reversed.
80-9x + 8 = 10(x) + 8-x

88 - 9x = 9x + 8

18x = 80

x = 

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