Does that clue work properly? You need an 'e' for Enigma, so can't take out the E for East or for the E being at the eastern side of the word 'imagine'. It's an I that needs to go, isn't it?
Marytobin, Yes, I knew the answer would be Enigma, but it's a poorly constructed clue - it doesn't work for me! I should have remembered that the RTE clues aren't always … conventional.