The Earth formed by accretion of Moon-to Mars-size embryos coming from various heliocentric distances. The isotopic nature of these bodies is unknown. However, taking meteorites as a guide, most models assume that the Earth must have formed from a heterogeneous assortment of embryos with distinct isotopic compositions(1-3). High-precision measurements, however, show that the Earth, the Moon and enstatite meteorites have almost indistinguishable isotopic compositions(4-10). Models have been proposed that reconcile the Earth-Moon similarity with the inferred heterogeneous nature of Earth-forming material, but these models either require specific geometries for the Moon-forming impact(11,12) or can explain only one aspect of the Earth-Moon similarity (that is, O-17)(1-3). Here I show that elements with distinct affinities for metal can be used to decipher the isotopic nature of the Earth's accreting material through time. I find that the mantle signatures of lithophile O, Ca, Ti and Nd, moderately siderophile Cr, Ni and Mo, and highly siderophile Ru record different stages of the Earth's accretion; yet all those elements point to material that was isotopically most similar to enstatite meteorites. This isotopic similarity indicates that the material accreted by the Earth always comprised a large fraction of enstatite-type impactors (about half were E-type in the first 60 per cent of the accretion and all of the impactors were E-type after that). Accordingly, the giant impactor that formed the Moon probably had an isotopic composition similar to that of the Earth, hence relaxing the constraints on models of lunar formation. Enstatite meteorites and the Earth were formed from the same isotopic reservoir but they diverged in their chemical evolution owing to subsequent fractionation by nebular and planetary processes(13).