I need two three digits numbers, Please respond!

OK , here the question word for word: What are two three digit numbers, M and N, such that
A. The difference between M and N is a three digit perfect square.
B. The difference between the squares of M and N is either one more than or one less than the product of M and N

Hints
One of the numbers is prime
Each number has two digits that are the same
Neither number is a palindromic number
The last digit of one number is the first digit of the other
The last digit of the prime number is the first digit of the composite number
The smaller number is the prime number
Of the six digits only one is an even number
A factor of the composite number is 13

I am stumped here, Any help is welcomed!
Thanks!

The answer is 377 and 233. 377-233 = 144. 377^2 - 233^2 = 87840. 377*233 = 87841. This took me forever :)

your hint "The last digit of one number is the first digit of the other"
Does this means the same as "The last digit of the prime number is the first digit of the composite number" ?

Or does it mean that the first digit of the prime number is the last digit of the composite number too?

377 and 233

pain old guess and check, the only saving grace was one number had to be a multiple of 13. i could not figure it algebraically.