lipogram

[Tenshi]

lipogram

\Lip"o*gram\ (l[i^]p"[-o]*gr[a^]m; 277), n. [Gr. lei`pein, lipei^n, to leave, omit + -gram.] A writing composed of words not having a certain letter or letters; -- as in the Odyssey of Tryphiodorus there was no A in the first book, no B in the second, and so on.

Anyone interested in doing this?

and example that I came up with (as I was helping my cousin to figure out how to write one)

Contorting through a world
Gnawing at a mind
Slight consolation I am told
As I cannot find
A way in this world...

Where I have excluded all 'e' in the text