Answer
$\Delta V = 8200~V$
Work Step by Step
We can find the potential difference:
$U = \frac{1}{2}C~(\Delta V)^2$
$(\Delta V)^2 = \frac{2~U}{C}$
$\Delta V = \sqrt{\frac{2~U}{C}}$
$\Delta V = \sqrt{\frac{(2)(300~J)}{9\times 10^{-6}~F}}$
$\Delta V = 8200~V$