x[t_, s_] = ((E^t)) (((1 + (s^2))/s)) - 
        (1/s)
y[t_, s_] = ((E^t)) ((s/(Sqrt[1 + (s^2)]))) + 
        1 - ((s/(Sqrt[1 + (s^2)])))
u[t_, s_] = 
      2 (Sqrt[ 1 + 
                (s^2)]) (E^(2  t)) - (Sqrt[1 + (s^2)])
ParametricPlot3D[{x[t, s], y[t, s], u[t, s]}, {s, -10, 
        10}, {t, -10, 10}, 
      PlotRange -> {{-10, 10}, {-10, 10}, {-10, 10}}, 
      ViewPoint -> {-2, -2, 0}]