Eduard Orel grew up Nový Jičín and Opava. He joined the navy and took part in the Battle of Lissa (the island of Vis) in 1866. Here he attained the rank of Naval cadet. In 1872 Orel got the chance to participate in the exploration expedition to the North Pole, led by Julius von Payer (1842–1915) and Carl Weyprecht (1838–1881). Which, despite being trapped in ice floes and moving only slowly by drifting, discovered a new archipelago in late August 1873, which was named Franz Josef Land. The participants of the expedition explored also the southern part of the archipelago and named the different parts of it.
It was Eduard Orel who, together with Julius Payer and one of the sailors, reached the northernmost point on earth (82 degrees and 5 minutes) on 12 April 1874. During this adventurous sledge expedition, Orel saved Payer`s life. At the risk of his own life, he helped him when he was pinned by large block of ice. When Eduard Orel returned from the expedition, Emperor Franz Joseph I bestowed upon him the Order of the Iron Crown of the third class and promoted him to the nobility. Afterwards, Sir Orel served at the naval headquarters in Trieste, where he worked together with Julius von Payer and Carl Weyprecht for two years on the results of their polar expedition. The book was published by Julius Payer in 1876 under the title Die Österreichisch-Ungarische Nordpol-Expedition (The Austro-Hungarian Expedition to the North Pole). Its shortened version was published in Czech under the title Captured in the Ice and became very popular. Sir Orel then left military service and in 1877 was appointed by Crown Prince Rudolph as administrator of Miramare Castle, where he died on 5 February 1892. The commemorative plaque to Eduard Orel was unveiled in Nový Jičín in 2014 on the initiative of the Club of Nový Jičín Friends and Patriots.