The two silvery-white metals discovered by English chemist Smithson Tennant with atomic numbers 76 and 77 are osmium (atomic number 76) and iridium (atomic number 77). These elements were identified by Tennant during his work with platinum samples in 1803. Osmium and iridium are both transition metals and are known for their dense and corrosion-resistant properties. They are often found together in nature and are used in various applications, including jewelry, electrical contacts, and catalysts.