Pablo Neruda's poem "Tonight I Can Write" is about the loss of the speaker's lover. The poem moves readers through the speaker's new ability to write about the painful experience of losing his or her lover. Prior to "tonight," the speaker is unable to write--too grief stricken to come to terms with what has happened.
In the line in question, "the same night whitening the same trees," personification is used. Whitening refers to something made white or pale. Here, it does not refer to the trees changing color naturally. Instead, it refers to the trees becoming pale because they are sick like the separated lovers. The whitening refers, then, to the paleness the trees, changed because the lovers are changed and "no longer the same."