Let x be first number and y- second number. When you subtract first square number from second you get [tex]y^2-x^2[/tex] and it is equal to 7.
Hence
[tex]y^2-x^2=7[/tex].
Find factors of right and left sides:[tex](y-x)(y+x)=1\cdot 7[/tex].
Since [tex]y+x\ \textgreater \ y-x[/tex] you have that
[tex] \left \{ {{y-x=1} \atop {y+x=7}} \right. [/tex].
Add these equations:
[tex]y-x+y+x=1+7, \\ 2y=8, \\ y=4[/tex].
Then x=7-y=7-4=3.
Answer: [tex]4^2-3^2=7.[/tex]
