Jamieson, Fausset and Brown on Numbers 20:14-16

14-16. Moses sent messengers ... to the king of Edom--The encampment at Kadesh was on the confines of the Edomite territory, through which the Israelites would have had an easy passage across the Arabah by Wady-el-Ghuweir, so that they could have continued their course around Moab, and approached Palestine from the east [Roberts]. The Edomites, being the descendants of Esau and tracing their line of descent from Abraham as their common stock, were recognized by the Israelites as brethren, and a very brotherly message was sent to them.