Matrices & Systems · Hard problem

A recycling plant processes two input material streams – stream $1$ and stream $2$ – through two sequential sorting stages. Stage $1$ redistributes the incoming tonnage according to $R = \begin{pmatrix}1 & 2\\3 & 1\end{pmatrix}$ (stream $1$'s tonnage becomes the first row's combination, stream $2$'s the second's), and stage $2$ further redistributes the result according to $F = \begin{pmatrix}2 & 0\\1 & 1\end{pmatrix}$. The two final measured outputs, after both stages, are $18$ tons and $26$ tons. How many tons of stream $1$ originally entered the plant?