let the original 2-digit number have the digits 'x' and 'y' that is, is written in the form: 10*x + y

x and y are elements of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

by swapping x and y we get the following number: 10*y + x

the new number is 30 less than the original number

10*y + x = 10*x + y - 30

9*x - 9*y = 30

3(x - y) = 10

x - y = 10/3

x and y are integers then x - y is integer as well

since the right side 10/3 is not an integer we conclude that this equation has no solutions thus

there is no such number.