Problem 452

Suppose that the original integer has tens digit $a$ and ones (units) digit $b$. This integer is equal to $10 a+b$. When the digits are reversed, the tens digit of the new integer is $b$ and the ones digit is $a$. This new integer is equal to $10 b+a$. Since the new two-digit integer minus the original integer is 54, then $(10 b+a)-(10 a+b)=54$ and so $9 b-9 a=54$ which gives $b-a=6$. Thus, the positive difference between the two digits of the original integer is 6.