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The solve command looks for an analytic solution. In this case, the solution will involve the Lambert W function, lambert_w. For some reason, though, Sage is not finding it. (You need to use to_poly_solve=True in the solve command, but Sage is encountering an error.)
To find approximations of the solutions, you can use find_root.
For example,
find_root(-V+exp(V)-0.5*V-1,-1,0.5)
and
find_root(-V+exp(V)-0.5*V-1,0.5,1)
give the two roots.
