These poems are not so much an escape from or denial of emotion as they are mode of expressing it that is different from that of most poetry written prior to the year 1900.

Eliot, in both "Prufrock" and "The Waste Land," does in fact deal with emotional themes: regret, loss, alienation, embarrassment. But he uses an impersonal style of conveying them. Prufrock is presented as a little man who frets over little things which reveal his self-abasement and, by extension, the disordered and despairing world of the modern age. But Eliot distances himself, personally, from this through the remoteness of the Prufrock persona and the deliberately un-poetic language, as in the famous opening:

Let us go then, you and I,
When the evening is spread out against the sky,
Like a patient etherized upon a table.

This poem, with its epigraph from Dante and its references to "eating a peach" and women who come and go "talking of Michelangelo," is one of alienation. Similarly, "The Waste Land" is filled with remote allusions and descriptions of ghost-like populations with whom the poet cannot commune:

A crowd flowed over London bridge, so many,
I had not thought death had undone so many.

Wilfred Owen's verse is more "conventional" and less modernist, but the horrors of war are described in an impersonal, matter-of-fact way that drives home the point of the brutality of war even more strongly than personal outrage, more emotionally expressed, would do. Compare "Dulce et Decorum Est" with Thomas Hardy's "The Man He Killed." Both are anti-war poems, but even Hardy, as bleak and pessimistic as he is, presents a more gently regretful tone than that of Owen's despairing, hell-like vision.

T. S. Eliot developed his theory of impersonality in his essay "Tradition and the Individual Talent." In this essay, he states:

Poetry is not a turning loose of emotion, but an escape from emotion; it is not the expression of personality, but an escape from personality.

In this statement, he is articulating a combination of ideas. First, he does not think that poetry should resemble a diary in the sense of simply being an outpouring of what a person happens to be feeling at a given time. Instead, it exists at an intersection of the poetic tradition, the objective external objects or specific images that can evoke an emotion in a reader, and the particular emotion or experience.

Thus in "Prufrock," we do not simply get an outpouring of Eliot's own feelings. The poem connects to tradition through its frequent uses of allusion as well as its formal character, which moves back and forth between modernist free verse and traditional forms such as the heroic couplet and Shakespearean song. 

Although "The Wasteland" may have originated in Eliot's personal feelings (instead of being purely autobiographical), it addresses fragmentation as a modern condition and grounds itself in poetic and religious tradition in its central figure of the Fisher King. 

"Dulce et Decorum Est” is a more intensely personal poem, but the poet distances himself by use of the concrete imagery and details that are "linguistic objective correlatives" of the emotions experienced. Rather than telling us that war is horrible, Owens shows its horrors by means of precise descriptions of soldiers enduring trench warfare and gas attacks in World War I. Its title and conclusion link it to the poetic tradition.