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The required two numbers are 6 and 8.
Let us denote the required numbers by c and d.
Given that the difference between two natural numbers is 2.
If we assume d > c, then d – c = 2
⇒ d = 2 + c → equation 1.
Also given that the sum of their squares is 100.
⇒ c² + d² = 100
⇒ c² + (2 + c)² = 100 (using the value of d from equation 1)
⇒ 2c² + 4c + 4 = 100
⇒ 2c² + 4c = 96
⇒ 2c(c+2) = 96
⇒ c(c+2) = 48
Using the factorization for 48, we get 6 × 8 = 48
⇒ c = 6
⇒ c+2 = 8
⇒ d = 8
Therefore, the required two numbers are 6 and 8.
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