The sum of two number, when multiplied with each of the number separately, then the results of these multiplication are 2418 and 3666, respectively. Find the difference between the numbers.?

Let the number be x and y.
Now, according to the question,
x(x + y) = 2418 .....(i)
and y(x + y) = 3666 .....(ii)
On adding Eqs. (i) and (ii), we get
x² + xy + yx + y² = 6084
⇒ x² + 2xy + y² = 6084
⇒ (x + y)² = 6084
∴ x + y = √6084 = 78
On subtracting Eq. (ii) from Eq. (i), we get
x² + xy - yx - y² = -1248
⇒ x² - y² = -1248
⇒ (x + y) (x - y) = -1248
⇒ 78(x - y) = -1248
⇒ x - y = - 1248 / 78 = -16
⇒ (y - x) = 16