Two ideal emf devices are connected to a set of resistors as shown in the figure below. If $\mathcal{E}_1 = 3.50 \text{ V}$, $R_1 = 12.00 \Omega$, $R_2 = 6.00 \Omega$, $R_3 = 17.00 \Omega$, $R_4 = 19.50 \Omega$, and the current through $R_4$ is $0.260 \text{ A}$, what is the emf $\mathcal{E}_2$?