Question 1163433
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            The solution by @josgarithmetic has an error.


            I came to bring a correct solution.



<pre>
Let x be the smaller number; then the greater number is (x+4).


You have this equation

    x^2 + (x+4)^2 = 72.


Simplify and solve using the quadratic formula

    x^2 + x^2 + 8x + 16 = 72

    2x^2 + 8x - 56 = 0

    x^2  + 4x - 28 = 0

    {{{x[1,2]}}} = {{{(-4 +- sqrt(4^2 +4*28))/2}}} = {{{(-4 +- sqrt(128))/2}}} = {{{(-4 +- 8*sqrt(2))/2}}} = {{{-2 +- 4*sqrt(2))}}}.


So, the numbers are  {{{x[1]}}} = {{{-2 + 4*sqrt(2)}}}  and  {{{x[2]}}} = {{{-2 - 4*sqrt(2)}}}.      <U>ANSWER</U>
</pre>

Solved and completed.