"Joshua then began a diligent search to find out the guilty one. He took Israel by their tribes, then by their families, and next individually; and Achan was designated as the guilty one. But that the matter might be plain to all Israel, that there should be no occasion given them to murmur and to say that the guiltless was made to suffer, Joshua used policy. He knew Achan was the transgressor and that he had concealed his sin and provoked God against His people. Joshua discreetly induced Achan to make confession of his sin, that God's honor and justice might be vindicated before Israel. “And Joshua said unto Achan, My son, give, I pray thee, glory to the Lord God of Israel, and make confession unto Him; and tell me now what thou hast done; hide it not from me. 3T 268.1"
"So Joshua rose up early in the morning, and brought Israel by their tribes; and the tribe of Judah was taken: And he brought the family of Judah; and he took the family of the Zarhites: and he brought the family of the Zarhites man by man; and Zabdi was taken: And he brought his household man by man; and Achan, the son of Carmi, the son of Zabdi, the son of Zerah, of the tribe of Judah, was taken."
EGW recounts the story of Achan and Joshua's method of finding the guilty party, referencing Joshua's plea to Achan to confess. While not a direct quote of Joshua 7:16-18, it accurately reflects the events described in those verses and the surrounding narrative.