Question 1111018
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You have received two good solutions, very similar to each other, from other tutors.<br>
Here is a suggestion for a different approach you might find easier.<br>
Let the two numbers we are looking be x and y.  We know {{{1/x+1/y = 7}}} and {{{1/x-1/y = 3}}}.<br>
Working with fractions is more difficult than working with whole numbers.  So<br>
let a = 1/x
let b = 1/y<br>
then the two equations are
{{{a+b = 7}}} and {{{a-b = 3}}}<br>
That pair of equations is easily solved to find a=5 and b=2.<br>
Then, to finish the original problem,
x = 1/a = 1/5
y = 1/b = 1/2<br>
The two numbers are 1/5 and 1/2.