Question: expressing function with series

I got a function to express v*t=(S0-St)+Km*ln(S0/St). The only unknown here is St. I solve it for St and get

St=LambertW((S0*e)/Km)*Km)

And I need to express this in rows then t=0..x (t=time) I know I should use series or asympt because t is variable, but I keep getting errors. Is there any way to express this function in rows??and 2nd question would be can I solve the function to find St without that LambertW. If so how do I do it.

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