Please, how is the equation system below named exactly (to search further literature)? Does it have an analytical solution? If it doesn't, then what could be the fastest numerical method for it (preferrably, with some available C++ implementation)? All the big letters (A, ... , I) are known values.

$(A*x-B*y)^{2}+(C*x-D*y)^{2}+(x-y)^{2}=G$ $(A*x-E*z)^{2}+(C*x-F*z)^{2}+(x-z)^{2}=H$ $(E*z-B*y)^{2}+(F*z-D*y)^{2}+(z-y)^{2}=I$

BTW it is related to inverse-projecting a 3D triangle based on the screen image + knowing the triangle's edges. Intuitively (maybe I'm wrong), it should have 2 answers (x,y,z). And if it helps somehow, I actually only need the values of $(x-y)/(C*x-D*y)$