x[t_, 
        s_] = ((E^t)) ((((Sqrt[2]) + (Sqrt[2 - 4  s (Sqrt[ 2])]))/2)) + s - ((((Sqrt[2]) + (Sqrt[2 - 4  s (Sqrt[ 2])]))/2))
y[t_, 
        s_] = ((E^t)) ((((Sqrt[2]) - (Sqrt[2 - 4  s (Sqrt[ 2])]))/2)) + s - ((((Sqrt[2]) - (Sqrt[2 - 4  s (Sqrt[ 2])]))/2))
u[t_, s_] = 
      2 (Sqrt[ 2]) (E^(2  t)) s - (Sqrt[2]) s
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}]