let the two digit number be 10*a + b that is 'a' is on the tens' place and 'b' is in the ones' place. a and b are elements of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, a <>0

the sum of the digits of a two digit number is 13

a + b = 13

twice the first digit is 1 less than the second digit

a = b - 1

by solving the system of equations

a + b = 13

a = b - 1

we find

a = 6

b = 7

thus the two digit number is 67.