"I saw that many have taken advantage of what God has shown in regard to the sins and wrongs of others. They have taken the extreme meaning of what has been shown in vision, and then have pressed it until it has had a tendency to weaken the faith of many in what God has shown, and also to discourage and dishearten the church. With tender compassion should brother deal with brother. Delicately should he deal with feelings. It is the nicest and most important work that ever yet was done to touch the wrongs of another. With the deepest humility should a brother do this, considering his own weakness, lest he also should be tempted. 1T 166.1"
"Brethren, if a man be overtaken in a fault, ye which are spiritual, restore such an one in the spirit of meekness; considering thyself, lest thou also be tempted."
Galatians 6:1 directly addresses restoring a brother overtaken in a fault with meekness and self-awareness, which is precisely the principle EGW is elaborating on.
"Moreover if thy brother shall trespass against thee, go and tell him his fault between thee and him alone: if he shall hear thee, thou hast gained thy brother."
Both passages discuss dealing with a brother's faults. Matthew 18:15 outlines the process, while EGW emphasizes the spirit in which it should be done (tender compassion, humility).
"I have seen the great sacrifice which Jesus made to redeem man. He did not consider His own life too dear to sacrifice. Said Jesus: “Love one another, as I have loved you.” Do you feel, when a brother errs, that you could give your life to save him? If you feel thus, you can approach him and affect his heart; you are just the one to visit that brother. But it is a lamentable fact that many who profess to be brethren, are not willing to sacrifice any of their opinions or their judgment to save a brother. There is but little love for one another. A selfish spirit is manifested. 1T 166.2"
"This is my commandment, That ye love one another, as I have loved you."
EGW directly quotes John 15:12.
"Hereby perceive we the love of God, because he laid down his life for us: and we ought to lay down our lives for the brethren."
Both passages discuss laying down one's life for others, reflecting the love of Christ. EGW expands on the practical application of this principle.
"Look not every man on his own things, but every man also on the things of others."
Both passages emphasize considering the needs of others rather than being self-centered. EGW's discussion of selfishness and lack of love connects to the principle of looking out for others' interests.