If we divide a two-digit number by a number consisting of the same digits written in the reverse order, we get 1 as a quotient and 18 as a remainder. If we add 33 in the given number, we get the sum of the squares of the digits constituting that number. Find the number.

Let the number be 10x + y, so we can write 10x + y = 10y + x + 18, which simplifies to x - y = 2. Testing 97, dividing 97 by 79 gives a quotient of 1 and a remainder of 18. Furthermore, adding 33 to 97 gives 130, and the sum of the squares of its digits is 9 squared plus 7 squared, which also equals 130. Therefore, the required number is 97.

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