She showed me a letter written in English.

Literal

She [topic-は] me [to-に] English [in-で] was-written letter [object-を] showed.

A passive relative clause modifying 手紙 ('letter'). The clause [英語で書かれた] = 'written in English' modifies the letter as a single unit. 書かれた is the past passive of 書く ('write') — agentless passive, since the writer's identity isn't relevant. The で here is the means/manner particle ('in English'), parallel to ペンで書く ('write with a pen'). Note the lack of an explicit subject in the relative clause — typical of Japanese, where the modified noun (手紙) implicitly fills the relevant role.