We present new experimentally measured and theoretically calculated rate coefficients for the electron-ion recombination of W$^{18+}$([Kr] $4d^{10}$ $4f^{10}$) forming W$^{17+}$. At low electron-ion collision energies, the merged-beam rate coefficient is dominated by strong, mutually overlapping, recombination resonances. In the temperature range where the fractional abundance of W$^{18+}$ is expected to peak in a fusion plasma, the experimentally derived Maxwellian recombination rate coefficient is 5 to 10 times larger than that which is currently recommended for plasma modeling. The complexity of the atomic structure of the open-$4f$-system under study makes the theoretical calculations extremely demanding. Nevertheless, the results of new Breit-Wigner partitioned dielectronic recombination calculations agree reasonably well with the experimental findings. This also gives confidence in the ability of the theory to generate sufficiently accurate atomic data for the plasma modeling of other complex ions.