We study with unprecedented detail the chemical composition and stellar parameters of the solar twin 18 Sco in a strictly differential sense relative to the Sun. Our study is mainly based on high resolution (R ~ 110 000) high S/N (800-1000) VLT UVES spectra, which allow us to achieve a precision of about 0.005 dex in differential abundances. The effective temperature and surface gravity of 18 Sco are Teff = 5823+/-6 K and log g = 4.45+/-0.02 dex, i.e., 18 Sco is 46+/-6 K hotter than the Sun and log g is 0.01+/-0.02 dex higher. Its metallicity is [Fe/H] = 0.054+/-0.005 dex and its microturbulence velocity is +0.02+/-0.01 km/s higher than solar. Our precise stellar parameters and differential isochrone analysis show that 18 Sco has a mass of 1.04+/-0.02M_Sun and that it is ~1.6 Gyr younger than the Sun. We use precise HARPS radial velocities to search for planets, but none were detected. The chemical abundance pattern of 18 Sco displays a clear trend with condensation temperature, showing thus higher abundances of refractories in 18 Sco than in the Sun. Intriguingly, there are enhancements in the neutron-capture elements relative to the Sun. Despite the small element-to-element abundance differences among nearby n-capture elements (~0.02 dex), we successfully reproduce the r-process pattern in the solar system. This is independent evidence for the universality of the r-process. Our results have important implications for chemical tagging in our Galaxy and nucleosynthesis in general.