The Burning Crown quest can only be found on the main map in the Top-Right quadrant of the quest map. you can access it after beating the Baron Castle quests and specifically after beating the ogre in the Lord Maxom quest. Burning Crown quest takes 10 energy per quest and takes 20 quests to complete for a grand total of 200 energy to complete. Burning Crown Shard used for Alchemy can only be found during this quest.