Question 963543
Denote your numbers a, b.
{{{a + b = 43}}}
and 
{{{a*b = 450}}}
Thus
{{{a(43-a)=450}}}
{{{43a-a^2-450=0}}}
{{{a^2-43a+450=0}}}
{{{(a-18)(a-25)=0}}}
Thus a = 18 or a = 25. This means b = 43 - 18 = 25 or b = 43 - 25 = 18, respectively. The absolute value of the difference between the numbers would be 7.
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