for the first one, have you used the Lambert W function before?
for the second,
Find the inverse function of f(x)=e^x+x.
by the way, plz help me solve this exercise: A particle is traveling upward and to the right along the curve y= lnx. Its x-coordinate is increasing at the rate (dx/dt)= x^(0.5) m/sec. At what rate is the y-coordinate changing at the point (e^2; 2)?