6. Find a two-digit number if it is known that the sum of its digits is 13, and the difference between the sought number and the number written with the same digits but in reverse order is a two-digit number with 7 units.
6. The desired number $N=10 x+y$, where $x=1,2,3,4,5,6,7,8,9 ; y=0,1,2$, $3,4,5,6,7,8,9$. Let's write down the two-digit numbers whose sum of digits is 13. Such numbers will be $49,58,67,76,85,94$. Let's write down the reversed numbers: $94,85,76,67,58,49$. The condition of the problem is satisfied only by the pair of numbers 85 and 58. $85-58=27$. The desired number $N=85$.