First, it is explicitly written in NT Scripture that Jesus claimed to be God: περὶ βλασφημίας, καὶ ὅτι σὺ ἄνθρωπος ὢν ποιεῖς σεαυτὸν θεόν. John 10:33
Second, Jesus claiming to be Son of God in v. 36 is in the context of the gods who are sons of God in Psalm 82 which Jesus himself quoted as Scripture. Jesus himself understood the accusation of blasphemy in light of Psalm 82:6 (blasphemy.....you makest thyself God....Say ye of him....thou blasphemest, because i said I am the Son of God?):
Psalm 82:6
6 I have said: You are gods and all of you the sons of the most High.
John 10
32 Jesus answered them, Many good works have I shewed you from my Father; for which of those works do ye stone me?
33 The Jews answered him, saying, For a good work we stone thee not; but for blasphemy; and because that thou, being a man, makest thyself God.
34 Jesus answered them, Is it not written in your law, I said, Ye are gods?
35 If he called them gods, unto whom the word of God came, and the scripture cannot be broken;
36 Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest; because I said, I am the Son of God?
and third, this is again reiterated in the gospel's inclusio:
The Word was God (John 1:1)
In him was life (John 1:4)
Believe in his name (John 1:12)
Epilogue of John:
That you may believe
Jesus Christ, the Son of God
that by believing you may have
life in his name (John 20:31)
The inclusio in the Gospel of John reveals that "Belief in Jesus as both God and Son to have Life" is the gospel's purpose.
