  Based on the Hugenholtz-Van Hove theorem, it is shown that both the symmetry
energy E$_{sym}(\rho)$ and its density slope $L(\rho)$ at normal density
$\rho_0$ are completely determined by the global nucleon optical potentials
that can be extracted directly from nucleon-nucleus scatterings, (p,n) charge
exchange reactions and single-particle energy levels of bound states. Adopting
a value of $m^*/m=0.7$ for the nucleon effective k-mass in symmetric nuclear
matter at $\rho_0$ and averaging all phenomenological isovector nucleon
potentials constrained by world data available in the literature since 1969,
the best estimates of $E_{sym}(\rho_0)=31.3$ MeV and $L(\rho_0)=52.7$ MeV are
simultaneously obtained. Uncertainties involved in the estimates are discussed.
