She was a friend and influencer of the travel writers and artists Marianne North and Isabella Bird.
Eka's grandfather Sir Alexander Cumming inherited the wealth of his wife and the name and arms of Gordon of Gordonstoun in 1804 and used the hyphenated double surname which was not consistently used by family members.
A Swiss maid, Cherie, taught her French and after the death of her mother in 1848, she went to live with an aunt in Northumberland.
Many of her family members were travellers, an uncle Charles Cumming-Bruce married the grand-daughter of the Nile explorer James Bruce of Kinnaird.
Her travelling phase began around 1866 when she was in Loch Ness where her terminally ill brother Roualeyn was being nursed by another sister.
She taught herself how to paint, and had help from artists visiting her home, including one of Queen Victoria's favorite painters, Sir Edwin Landseer.
She also took an invitation from her half-sister Emilia Sergison to visit India and after spending a year there she wrote In the Himalayas and on the Indian Plains (1884).
The latter book resulted from an invitation to join a French ship put into service for the Bishop of Samoa so that he could visit remote parts of his far-flung diocese.
Miss Gordon-Cumming received much criticism from male writers of the era, perhaps because she did not fit in the traditional Victorian role of women, as she often traveled alone and unaided.