My question is.. A rich merchant had collected many gold coins. He did not want to tell his wife.So he makes it tricky.He says'if I divide coins into two unequal numbers , then 48 times the difference between the two numbers will be equal to the difference between square of two numbers.' We have to find the number of gold coins.

What do YOU think ?
While we're happy to help, we wont do all the work for you.

I suggest you start by setting up an equation for the two piles of coins, and see if it can be simplified to yield an answer for the sum of the two piles.