The award of a DFC to Lieut Edward Enos Arnold was announced in London Gazette 1st January 1919. The decoration was for distinguished and gallant services in Egypt. He was presented with the cross by His Majesty King George V at Buckingham Palace on 4th December 1919. There was no published citation.
As suggested by previous respondents, the next step will take you to the Public Record Office.
Incidentally, noting that your surname is Crane, you might be interesting in taking a look at my website. It has a couple of images of the military funeral (1918) of Mortimer Park Crane, taken from a rather unusual photograph album that I have in my collection.
http://www.routledgeh.freeserve.co.uk/inde...dex.htm
Hope you find this of interest. Hylton