As Jesus gets deeper into conversation with the Pharisees in John 8, His self-understanding becomes more explicit. At two junctures in today's passage, Jesus refers to Himself as "I AM". This of course hearkens to the tetragrammaton in Exodus 3, where Yahweh tells Moses "I AM." Much has been written over the years on the meaning of the sacred name of God. This was held to be so sacred in ancient Israel, and by many Jewish people right up to our day, that it is not uttered. Even the word God is sometimes written as G-d.
Jesus unequivocally identifies Himself with God by claiming identity with I AM. Some translations render verses 24 and 28 as Jesus saying "I am he." This is effectively the same thing as saying I AM. The 'he' Jesus refers to is the Most High, the Blessed One. That point was certainly not missed by the audience. Jesus also identifies Himself in this passage as the Son of Man. Here is another claim to divinity, referencing the passage from Daniel 7, where one like a Son of Man comes and receives dominion. Adding more fuel to the fire, Jesus draws a connection between Himself and Moses lifting the bronze serpent (Numbers 21:4-9). As the Israelites were dying from snakebites, anyone who looked upon the bronze serpent held aloft on the pole by Moses would live. Thus, Jesus identifies Himself as the miraculous, divine source of life for those who are dying. It is in their sins that the Pharisees (and everyone else, for that matter) will die. We look to the Son of God, who is true God, as the source of our life and salvation from death. As the Lord says in this passage, He speaks what He hears and learns from the Father. Only He who is God can have such an intimate relationship with the Father so as to speak what He learns and hears in this manner.