"Let nothing disturb you. Let nothing frighten you. Everything passes away except God. God alone is sufficient."UPDATE, MYSTERY SOLVED: After I posted this quote over on Facebook, my Lutheran colleague, Abraham Allende, left these informative comments and has permitted me to share them here:
The mystic was not anonymous. She was St. Teresa of Avila, also known as Teresa of Jesus, a native of Spain, a member of the Carmelite order and a leader of the Catholic Reformation in the 16th Century (better known as the counterreformation). She is commemorated on October 15. The text that you quoted is a poem she wrote and used in a Taize song sung in Spanish: "Nada te turbe, nada te espante. Todo se pasa. Dios no se muda. Quien a Dios tiene, nada le falta. La paciencia todo lo alcanza. Solo Dios basta."
Sorry to go on and on but she is one of my favorite poets and people of faith. I am surprised that Norman Vincent Peale would not give her proper attribution and I won't speculate as to why.