Answer : $x^2-y^2=32$
The distance between the foci $=16$
(ie) $2ae=16$
$\Rightarrow ae=8$
Given eccentricity $'e'=\sqrt 2$
$\therefore a\sqrt 2=8$
$a=\large\frac{8}{\sqrt 2}$
$a^2=\large\frac{64}{2}$$=32$
$b^2=a^2(e^2-1)$
$\;\;\;\;=32[(\sqrt 2)^2-1]$
$b^2=32$
Hence the equation of the hyperbola is $\large\frac{x^2}{32}-\frac{y^2}{32}$$=1$
Or $ x^2-y^2=32$