Or HaChaim on Numbers 20:14/אור החיים על במדבר כ׳:י״ד

1 אחיך ישראל, אתה ידעת "your brother Israel; you are aware, etc." The reason that Moses underlined the brotherly connection between Edom and Israel was to remind Edom that the discomfort of travel Israel experienced now was not due to recent events but to their respective ancestor and that he considered both Israel and Edom as being involved in this equally. Abraham's descendants were supposed to experience exile according to Genesis 15. However, only the descendants of one of Isaac's sons had paid the price by being enslaved in Egypt. Esau and his descendants had not experienced any of that suffering. The least the Edomites could do now was to display some degree of brotherliness by allowing the Jewish people passage to their own heritage. Compare Bereshit Rabbah 82, on Genesis 36,8 where it is explained that the reason Esau emigrated was that he did not want to pay the debt Abraham had contracted for at the covenant between the pieces.

2אתה ידעת, these words were Moses' reminder to Edom that they had been well aware of the decree which was part of the above-mentioned covenant that Abraham's descendants were to be enslaved in a foreign country for an extended period. This was something that only the descendants of Esau knew about. All the other pagans had considered the enslavement of the Israelites in Egypt as one of the many accidents of history, and had thought that if the family of Jacob had not voluntarily migrated to Egypt they would never have wound up as slaves.

3וירדו אבותנו, "our ancestors descended, etc." This was in addition to the exile they experienced in Egypt. We have to understand this in light of Shabbat 10 where we are told that a person should not show favoritism to one of his children over the others; had Jacob not spent five pieces of silver more to make a coloured coat for Joseph our ancestors might not have had to descend to Egypt and to have wound up in exile there." Tossaphot already question that statement saying that G'd had decreed this exile long before Joseph and his brothers had been born, going back to the covenant between the pieces in Genesis 15. They answer that but for Jacob's' open display of discrimination between his sons, the decree could have been fulfilled in some other country where it would not have been accompanied by nearly the same degree of cruelty that the Jews experienced in Egypt. The fact that the location where G'ds's decree came true was Egypt added untold suffering. This is why Moses described the migration to Egypt as a "descent," adding וירעו אותנו המצרים, how the Egyptians had mistreated the Jewish people

4Moses also conveyed to the Edomites by his lengthy explanantion that the Israelites had paid the debt arising from that covenant in full and that this was why they were now entitled to take possession of the land of Canaan. When Moses added the words ימים רבים, he meant that it had taken the people a long time to discharge their debt under that covenant in full.