"But the life of John was not spent in idleness, in ascetic gloom, or in selfish isolation. From time to time he went forth to mingle with men, and he was ever an interested observer of what was passing in the world. From his quiet retreat he watched the unfolding of events. With vision illuminated by the divine Spirit, he studied the characters of men, that he might understand how to reach their hearts with the message of heaven. CT 446.1"
"Annas and Caiaphas being the high priests, the word of God came unto John the son of Zacharias in the wilderness."
While Luke 3:2 simply states that the word of God came to John in the wilderness, the EGW passage expands on this by describing how John used his time in solitude to observe the world and understand people, preparing him for his ministry. It provides context and detail to the brief biblical statement.
"Of Christ, Simeon said, “Lord, now lettest Thou Thy servant depart in peace, according to Thy word: for mine eyes have seen Thy salvation, which Thou hast prepared before the face of all people; a light to lighten the Gentiles, and the glory of Thy people Israel.” And the record declares, “Jesus increased in wisdom and stature, and in favor with God and man.” Luke 2:29-32, 52 . CT 446.2"
"Lord, now lettest thou thy servant depart in peace, according to thy word: For mine eyes have seen thy salvation, Which thou hast prepared before the face of all people; A light to lighten the Gentiles, and the glory of thy people Israel."
Ellen White directly references Luke 2:29-32 in this passage.
"Jesus and John were represented by the educators of that day as ignorant because they had not learned in the schools of the rabbis; but the God of heaven was their Teacher, and all who heard were astonished at their knowledge of the Scriptures. CT 446.3"
"And the Jews marvelled, saying, How knoweth this man letters, having never learned?"
Both passages address the astonishment of people at the knowledge of Jesus and John, despite their lack of formal rabbinical education. John 7:15 specifically mentions the Jews marveling at Jesus's knowledge, while the EGW passage generalizes this to both Jesus and John, attributing their wisdom to God as their teacher.