The easiest way to use the results is with NDSolveValue. You can give your favourite names to the solutions and use them as ordinary functions for calculation or plotting:
eqns = {y'[t] == -447.0 Exp[2.24 y[t]] y[t] + z[t],
z'[t] == (-z[t] + 20)/0.401, y[0] == 0, z[0] == 0};
{solX, solZ} = NDSolveValue[eqns, {y, z}, {t, 0., 100.}]
solX[3]
Plot[solZ[t], {t, 0, 40}, PlotRange -> All]
ParametricPlot[{solX[t], solZ[t] - 20}, {t, 0, 40}, AspectRatio -> 1]
