Question 1045481
Let:
x= 1st number
y= 2nd number

The sum of two numbers is 14 means {{{x+y=14}}} eq 1
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the sum of their sqaures is 100 means {{{x^2+y^2=100}}} eq2
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solve for y in eq 1 then substitute to eq 2
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y=14-x
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{{{x^2+(14-x)^2=100}}} then simplify
{{{x^2+(196-28x+x^2)=100}}}
{{{2x^2+196-28x=100}}}
{{{2x^2+196-28x-100=0}}}
{{{2x^2-28x+96=0}}}
use quadratic formula to get the value of x. either of the two values can satisfy the problem so choose any.
a=2
b=-28
c=96
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

x=6
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y=14-6
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y=8
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The two numbers are 6 and 8.