Two Festivals not Found in the Torah

PURIM

From the LDS BIBLE DICTIONARY - FEASTS
The Feast of Purim (called Mordecai’s Day, 2 Macc. 15: 36) was instituted by Mordecai and confirmed by Esther, to commemorate the overthrow of Haman and the failure of his plots against the Jews’ (Esther 9: 20-32). The name Purim ("Lots") was given in mockery of the lots Haman had cast to secure a day of good omen for his enterprise (Esther 3: 7). The feast was held on the 14th and 15th of Adar (the twelfth month). The 13th of Adar, which was originally a feast to commemorate Nicanor’s death (1 Macc. 7: 49; 2 Macc. 15: 36), afterwards became a fast, called the Fast of Esther, in preparation for the feast. During the feast the whole book of Esther was read in the synagogues, and all Israelites - men, women, children, and slaves - were required to be present. The reading was accompanied by clapping of hands, stamping of feet, and clamorous curses on Haman and the Jews’ enemies, and blessings on Mordecai, Esther, etc. The feast was celebrated with great joy, shown by distributing gifts.

From EASTON'S BIBLE DICTIONARY - Purim
Pur, Purim - a lot, lots, a festival instituted by the Jews (Esther 9:24-32) in ironical commemoration of Haman's consultation of the Pur (a Persian word), for the purpose of ascertaining the auspicious day for executing his cruel plot against their nation. It became a national institution by the common consent of the Jews, and is observed by them to the present day, on the 14th and 15th of the month Adar, a month before the Passover.

CHANUKAH - Feast of the Dedication

From the LDS BIBLE DICTIONARY - FEASTS
"The Feast of the Dedication was instituted in the days of Judas Maccabaeus to commemorate the dedication of the new altar of burnt offering after the profanation of the temple and the old altar by Antiochus Epiphanes. The feast began on the 25th Chisleu, the anniversary of the profanation in 168 B.C., and the dedication in 165 B.C., and lasted eight days, during which no fast or mourning for any calamity or bereavement was allowed. It was kept like the Feast of Tabernacles with great gladness and with the bearing of the branches of palms and of other trees. There was also a general illumination, from which circumstance the feast received the name Feast of Lights."

When the Israelites were ready to rededicate the temple, they could only find one day's worth of consecrated oil with which to light the temple lamps. In faith they sent runners to find more oil and proceeded with the dedication. That one day's worth of oil remained lit for eight days, at which time runner returned with more oil.