This poem is all about silence. The speaker and his friend parted in "silence," and now apparently are no longer speaking to one another. He grieves in silence. If he ever meets her again, he's not planning on saying or doing anything other than silently crying in front of her (now that sounds like a hoot). In this poem, silence is both an expression of intense grief (they were so upset, when they left each other they couldn't even speak) and a way of hiding one's feelings (the speaker appears to not want anybody to know he's grieving, for various reasons).
Lines 1-2: The speaker and the woman parted in "silence." Right off the bat, silence and sadness are associated with one another.
Lines 3-4: The speaker and the woman are saying goodbye for years, or rather they're going to be "silent" for quite some time.
Line 25: "Secrecy" is just a different kind of silence. It's sort of like a metaphorical silence. While the speaker and his love interest certainly talked to one another, nobody knew they were meeting, so they were socially "quiet" about it. Silence = secrecy = something fishy is going on here.
Line 26: The speaker refuses to grieve out loud or publicly. He grieves in silence. It's like he doesn't want anybody to know the truth so he's keeping his mouth shut. This is both respectful to the woman—whose "shame" could get worse if everybody knew the truth about her—and the speaker and a way to avoid communicating one's feelings to people who might be able to help.
Lines 31-32: If the speaker meets or reconnects with the woman, he will greet her in the same way they parted: with silence and tears. So, the reunion will be just like the departure. Hmm, that's weird. It seems that here silence is partly the speaker's way of expressing anger, frustration, or displeasure with the woman.