How do I change parametric in t to cartesian when I can't re-arrage for t

Question

I'm stuck looking at this parametric equation which I have to put in cartesian form

$x=t^2+ \frac1t$, $y=t^2-\frac 1t$

Something to do with difference of two squares? I can't see how to eliminate $t$

$xy=t^4-\frac{1}{t^2}$ doesn't help.

I found something similar but couldn't apply it (as far as I could see) to this problem:

How do I change this parametric equation: $x=t+1/t, y=t^2 + 1/t^2$ into a Cartesian equation?

Thanks in advance! Rob

Answer 1

Hint: $x-y=\frac{2}{t}$ hence $t=\frac{2}{x-y}$.