So $12$% of the required number is $\sqrt{22+8\sqrt{16}} - \sqrt{22-8\sqrt{16}}$. I was initially defining the first part of the term as $x$ and the second as $y$ and then raising both to the power of $2$. But that does not seem to do anything. So I just applied a brute force approach:
$\sqrt{22+8\sqrt{16}} = \sqrt{22+32}=\sqrt{54}$ and the other one is $i\sqrt{10}$. Therefore the solution is $25(\sqrt{6}-i\frac{1}{3} \sqrt{10})$. It looks a bit ugly and I am pretty sure there is a neater way to solve this.
Denote with $x$ the required number. Then you know that $$\frac{12}{100}x=\sqrt{22+8\sqrt{16}} - \sqrt{22-8\sqrt{16}}$$ which implies that $$x=\frac{100}{12}\left(\sqrt{22+8\sqrt{16}} - \sqrt{22-8\sqrt{16}}\right)$$