Charles Ellicott Commentary Numbers 29:7

"And on the tenth day of this seventh month ye shall have a holy convocation; and ye shall afflict your souls: ye shall do no manner of work;" — Numbers 29:7 (ASV)

The tenth day of this seventh month ...— The law regarding the observance of the great Day of Atonement is contained in Leviticus 16:0 and Leviticus 23:26-32. The sacrifices prescribed in Numbers 29:8-11, which are the same as those prescribed for the first day of the seventh month, were to be offered in addition to the sin offerings of atonement prescribed in Leviticus 16:0 and to the daily burnt offerings. (See Notes on Leviticus 16:0; Leviticus 23:26–32.)

And you shall afflict your souls.— See Leviticus 16:29. This affliction or humiliation appears to have included fasting , although the word that denotes fasting is not used, nor is there any express injunction regarding fasting in the Pentateuch.