<PRE><B>Question 1010951</B>
Find two numbers whose difference is 10 and the sum of whose squares is 250. 
x - y = 10
x = y + 10
------------------------------------------------------
Response to Comment, generally when you are dealing with word problems, you do discard the negative solution.
------------------------------------------------------
:
x^2 + y^2 = 250
replace x with (y+10)
(y+10)^2 + y^2 = 250
FOIL
(y+10)(y+10)
y^2 + 20y + 100 + y^2 = 25
Combine like terms
2y^2 + 20y + 100 - 250 = 0
2y^2 + 20y - 150 = 0
Factors 
(2y + 30)(y - 5) = 0
positive solution is what we want here
y = 5
Find x
x = 5 + 10
x = 15
:
:
Check in the 2nd equation
15^2 + 5^2 = 250
225 + 25 = 250</PRE>