[tex]xy=144\implies y=\dfrac{144}x[/tex]
[tex]x+y=30\implies x+\dfrac{144}x=30[/tex]
[tex]\implies x^2-30x+144=(x-24)(x-6)=0[/tex]
[tex]\implies x=24\text{ or }x=6[/tex]
In the case of [tex]x=24[/tex], we have [tex]y=\dfrac{144}{24}=6[/tex], so that [tex]x-y=18[/tex].
On the other hand, if [tex]x=6[/tex], then [tex]y=144[/tex]. But this breaks the condition that [tex]x>y[/tex].
