Can we obtain the relation between $x,y$ in terms of $a,b$ for which $ (a+x-y)(x+y)>b $? I have this condition
$$ (a+x-y)(x+y)>b ,$$
where $x,y$ are two positive parameters and $a,b$ are fixed positive numbers.

Are we able to obtain other simpler alternative relations between $x,y$ in terms of $a,b$ under which the given condition holds?


Rearranging the expression:
\begin{align*}
(a+x-y)(x+y)                              &> b\\
a(x+y)+(x-y)(x+y)                         &> b\\
ax+ay+x^2-y^2                             &> b\\
(x^2+ax)-(y^2-ay)                         &> b\\
(x^2+ax+a^2/4-a^2/4)-(y^2-ay+a^2/4-a^2/4) &> b\\
(x^2+ax+a^2/4)-a^2/4-(y^2-ay+a^2/4)+a^2/4 &> b\\
(x+a/2)^2-(y-a/2)^2                       &> b\\
\frac{(x+a/2)^2}{b}-\frac{(y-a/2)^2}{b}   &> 1,\text{ if $b>0$}\\
\end{align*}
So the relationship is that $(x,y)$ are points outside the horizontal hyperbola with center at $(-a/2,a/2)$ and semi-axis $\sqrt{b}$, if $b>0$ o inside the vertical hyperbola with center at $(-a/2,a/2)$ with semi-axis $\sqrt{-b}$, if $b<0$.
