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Let two digit number be 10x+y
Given 10x+y=(x+y)8−−−−−−−−(1)
⟹14∣x−y∣+2=100x+y, let x>y
⟹14(x−y)+2=10x+y
⟹4x−15y+2=0−−−−−−−−(2)
from (1) 2x=7y−−−−−−−−(3)
From (2) & (3)
14y−15y+2=0
y=2
When y=2,x=7
So number is 72.
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