When does "e" at the end of a noun change it to a verb?

I was wondering about adding an e at the end of a word to change it from a noun to a verb. For example, cloth to clothe, and breath to breathe. Is this some special rule, or a quirk to the English Language?

(The key elements of the answer to this question are given in the comments following it. This answer ties them together and adds some more detail.)

If you look at a fuller range of examples—

• calf, calve; grief, grieve; half, halve; life, live; proof, prove; safe, save; serf, serve; strife, strive (with some meaning drift); thief, thieve;

• advice, advise; clo[s]e, clo[z]e; glass, glaze; grass, graze; hou[s]e, hou[z]e; u[s]e, u[z]e;

• bath, bathe; breath, breathe; cloth, clothe; mouth[θ], mouth[ð]; sheath, sheathe; tooth, teethe (still retaining old ablaut); wreath, wreathe;

—then you notice several key points:

1. All examples end in -f, -[s], -th, not in any other consonants.
2. These consonants are always preceded by vowels, or, more rarely, by liquids (half, halve; serf, serve).
3. The voiced (-[v], -[z], -[ð]) counterparts are always found in verbs (whereas the unvoiced counterparts can be either nouns or adjectives, like close and safe).

The voicing alternation (like the vowel alternation of tooth, teeth(e)) is fossilized phonology of Anglo-Saxon. Robert Diamond’s grammar of the language gives part of the processes, clearly identifying the Anglo-Saxon fricatives (f, s, þ) as voicing between vowels:

He does not say (though from memory Henry Sweet does) that these sounds also voice in the context vowel-l/r-...-vowel.

Verb formation from nouns and adjectives created the intervocalic context in Anglo-Saxon, because the verbal suffixes were nearly all verb initial (e.g., infinitival -(i)an, first singular present -e, third plural present -on). (Moreover, the past tense -d- also created a context for voicing, as per Diamond’s cited passage.)

Together, these explain the three generalizations governing examples like the ones that the questioner gave:

1. As Diamond’s discussion implies, these are the only three sounds of Anglo-Saxon that voice intervocalically, -f, -s, -th, which is why all examples end in orthographic variants of these consonants. (E.g., there’s no pinch, pinge.)
2. The rule of voicing operated only in special circumstances (e.g., vowel-...-vowel, vowel-l/r-...-vowel). (E.g., there’s no rinse, rin[z]e.)
3. Voicing occurs in verbs as, in Anglo-Saxon, verb formation triggered voicing owing to the shape of the suffixes. (Nouns and adjectives could occur without suffixes.)

Time has gnawed away at the rich morphology of Anglo-Saxon, so that the verb endings are now gone. Nonetheless, their effect is still felt in a few examples that speakers simply have to memorize.