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**7 and 3 .**

The difference between two

= 7-3

= 4

7^2= 7*7 = 49

3^2= 3*3 = 9

Sum of their squares = 49+9

= 58

**Therefore, the two numbers are 7 and 3**

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Let the numbers be x and y

x-y=4

therefore, x=y+4

x²+y²=58

(y+4)²+y²=58

y²+8y+16+y²=58

2y²+8y=42(58-16)

2(y²+4y-21)=0

y²+4y-21=0/2

y²+7y-3y-21=0

y(y+7)-3(y+7)=0

(y+7)(y-3)=0

therefore,y=-7,3

as the nos are natural, y=3

x=3+4=7

x=7

y=3

x-y=4

therefore, x=y+4

x²+y²=58

(y+4)²+y²=58

y²+8y+16+y²=58

2y²+8y=42(58-16)

2(y²+4y-21)=0

y²+4y-21=0/2

y²+7y-3y-21=0

y(y+7)-3(y+7)=0

(y+7)(y-3)=0

therefore,y=-7,3

as the nos are natural, y=3

x=3+4=7

x=7

y=3