Curve problem $x = x_0 + te^{x_0+1}.$

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I'm studying characteristic curves in PDE. In one of the problems I was doing, I came up with the following characteristic equation: $$x = x_0 + te^{x_0+1}.$$ I need to isolate $x_0$ to proceed with the solution of the problem, because by the initial conditions the result is socked. Can you help me get around the problem?