Sum of two no is 1000 …

Let us suppose  that the numbers are x and y.
According to question it is given that
The sum of the two numbers is 1000.
Thus, we have x + y = 1000
The difference between the squares of the two numbers is 256000.
Therefore, we have x² - y² = 256000
{tex} \Rightarrow{/tex} (x + y)(x - y) = 256000
{tex}\Rightarrow{/tex} 1000(x - y) = 256000
{tex}\Rightarrow x - y = \frac{{256000}}{{1000}}{/tex}
{tex}\Rightarrow{/tex} x - y = 256
Therefore, we have two equations
x + y = 1000 ......(1)
x - y = 256 .....(2)
Here x and y are unknowns.
We have to solve the above equations for x and y.
Adding equation (1) and (2), we get
(x + y) + (x - y) = 1000 + 256
{tex}\Rightarrow{/tex} x + y + x - y = 1256
{tex}\Rightarrow{/tex} 2x = 1256
{tex}\Rightarrow x = \frac{{1256}}{2}{/tex}
x = 628
Substituting the value of x in the equation (1) we get, 
628 + y = 1000
{tex}\Rightarrow{/tex} y = 1000 - 628
{tex}\Rightarrow{/tex} y = 372
Therefore the numbers are 628 and 372.