Jamieson, Fausset and Brown on Leviticus 10:3

3. Moses said ... This is it that the Lord spoke ... I will be sanctified in them that come nigh me--"They that come nigh me," points, in this passage, directly to the priests; and they had received repeated and solemn warnings as to the cautious and reverent manner of their approach into the divine presence (Ex 19:22; 29:44; Le 8:35).

Aaron held his peace--The loss of two sons in so sudden and awful a manner was a calamity overwhelming to parental feelings. But the pious priest indulged in no vehement ebullition of complaint and gave vent to no murmur of discontent, but submitted in silent resignation to what he saw was "the righteous judgment of God" [Ro 2:5].