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You are looking for a numerical solution; solve wants to give you exact solutions, and cannot solve this system - even doing it "by hand" gives

sage: solve(eq1.subs(vd=solve(eq2,vd)[0].rhs()),id)
[id == 1/100000000000*e^(-500000/39*id + 10000/39) - 1/100000000000]

To find a root between two endpoints, use something like

sage: find_root(id == 1/100000000000*e^(-500000/39*id + 10000/39) - 1/100000000000,0,10)

Good luck!