She's coming back this Sunday — that is, on the 10th.

Literal

She [topic-は] this-coming Sunday, namely 10th [on-に] returns.

すなわち is a formal connective meaning 'namely, in other words, that is to say.' It introduces a clarifying restatement, equating two expressions. In writing, you'll find it in academic prose, definitions, and official notices; in speech it sounds polished and slightly literary. The pattern 'X、すなわちY' lets the speaker first give the everyday reference (this Sunday) and then pin it down precisely (the 10th) — useful when the audience may not have a calendar handy.