This is an (older) form of dative found in (usually monosyllabic) nouns.
Der Tisch - des Tisch(e)s - am Tisch(e) - den Tisch
Today, the 'e' in the dative form is usually left out. But depending on the rhythm of the sentence or the register of language used (poetic, ironic, etc.) you may still want to include it.
Here are more such cases:
Das Bad - des Bad(e)s - im Bad(e) - das Bad
Das Weib - des Weib(e)s - beim Weib(e) - das Weib
Das Tier - des Tier(e)s - vom Tier(e) - das Tier
Der Stock - des Stock(e)s - am Stock(e) - den Stock
Das Buch - des Buch(e)s - im Buch(e) - das Buch
You find this with male and neuter words, not with female ones.
Die Frau - der Frau - bei der Frau - die Frau
I believe, in the middle ages there was something like bey der frouwe, but I am not sure. Some medieaevalist will show up here and give more competent information.
Likewise it seems to be rarely applicable to words with more than one syllable:
Das Segel - des Segels
Segeles - dem Segel Segele - das Segel
Moreover, it seems that the modern German ear ist not any more used to this 'e' but in words that often appear in old texts, particulary stage plays, or wherever modern man gets in contact with older language. For example
Das Boot - des Boot(e)s - dem Boot(e) - das Boot
should technically be correct, but at least I personally have to struggle a lot to get used to it. It sounds a little bit overdone.
I see now that this topic actually has been discussed repeatedly in his forum. In this post: Wie wird die Redewendung "wie es im Buche steht" grammatisch gebildet? there is even a link to an entire scholarly paper on the topic. Probably it offers deeper insight than what I wrote here free-handedly.
And now I see that perhaps my impromptu theory of only monosyllabic words being affected could be disputed:
Das Gesetz - des Gesetzes - dem Gesetz(e) - das Gesetz