I have this set of two equations

\begin{eqnarray}
e^{-35 (y-x)} & = & \frac{x}{y} \tag{1} \\ 
\frac{e^{-90 x}-e^{-90 y}}{e^{-142 x}-e^{-142 y}} & = & \frac{1892}{1007} \tag{2}
\end{eqnarray}

in the two real variables $x,y$, moreover I know from the Physical origin of these equations that $x,y\in[0,1]$. I am interested in numerical solutions, however
Mathematica for example doesn't give a solution.

Any hints how I can proceed here?