Commentary for Kiddushin 48:8

The Talmud explains the midrashic origins of the dispute. The word “sending” is used both in the context of the slave and in the context of a woman being divorced. According to R. Shimon, just as a woman being divorced needs a document, so too a slave going free always needs a document.
R. Meir uses the order of the words in the verse to posit that he does not. The phrase begins with “to freedom” and therefore R. Meir holds that the slave is free right away, even without a deed.