One of the most striking predictions of Einstein's special theory of relativity is also perhaps the best known formula in all of science: E=mc(2). If this equation were found to be even slightly incorrect, the impact would be enormous--given the degree to which special relativity is woven into the theoretical fabric of modern physics and into everyday applications such as global positioning systems. Here we test this mass-energy relationship directly by combining very accurate measurements of atomic-mass difference, Delta(m), and of gamma-ray wavelengths to determine E, the nuclear binding energy, for isotopes of silicon and sulphur. Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1-Delta(mc2)/E=(-1.4+/-4.4)x10(-7), indicating that it holds to a level of at least 0.00004%. To our knowledge, this is the most precise direct test of the famous equation yet described.