Is there anyway to rewrite this system to a system of $Q_1$,$Q_2$,$Q_3$ and $Q_4$ instead? $a,b,c,d,m$ are real numbers.
$$\begin{align} a&=Q_1^2-Q_2^2-Q_3^2+Q_4^2+m\\ b&=2Q_1Q_2-2Q_3Q_4\\ c&=2Q_1Q_3+2Q_2Q_4\\ d&=Q_1^2+Q_2^2+Q_3^2+Q_4^2\\ \end{align}$$