I'm aware that burzum means darkness in The Black Speech.
Do we know what the opposite is? How is lightness written?
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As @Darkgamma says, we don't know. The closest we have would probably be ghâsh, which means fire, and one could probably guess that the characteristic of being fire-like would be something like ghâshum, but there is no empirical evidence for that, except that the suffix -um seems to mean -ness, as in burz- (meaning dark) + -um (meaning -ness), put together to form burzum.
That said, ghâshum would literally mean "the characteristic of being like fire," not literally "lightness."
In short: no.
In a bit long: not really, and some people have gone to the effort of analysing the Black Speech. In essence, the list of words we know thus far is rather scant:
-at infinitive suffix, or possibly a specialized "intentive" suffix indicating purpose: Ash nazg durbatulûk "one Ring to rule them all"
bagronk (DBS) "cesspool", possibly bag+ronk "cess+pool"
búbhosh (DBS) "great"
búrz "dark", (isolated from Lugbúrz, q.v.), burzum "darkness"
dug "filth", tentatively isolated from pushdug, q.v.
durb- "rule", infinitive durbat, only attested with suffixes: durbatulûk "to rule them all". The verb durb- is remarkably similar to Quenya tur- of similar sense. ghâsh "fire" (stated to be derived from the Black Speech, may or may not represent Sauron's original form of the word)
gimb- "find", infinitive gimbat, only attested with a pronominal suffix: gimbatul, "to find them"
glob (DBS) "fool"
gûl "any one of the major invisible servants of Sauron dominated entirely by his will" (A Tolkien Compass p. 172). Translated "wraith(s)" in the compound Nazgûl, "Ringwraith(s)".
hai "folk", in Uruk-hai "Uruk-folk" and Olog-hai "Troll-folk"; cf. also Oghor-hai.
ishi "in", a suffixed postposition: burzum-ishi, "in the darkness".
krimp- "bind", infinitive krimpat, only attested with a pronominal suffix: krimpatul, "to bind them"
lug "tower". Isolated from Lugbúrz, q.v.
Lugbúrz the Dark Tower, Sindarin Barad-dûr (Lug-búrz "Tower-dark")
nazg "ring": ash nazg "one ring", Nazgûl "Ring-wraith(s)"
Nazgûl "Ring-wraith(s)", nazg + gûl (q.v.)
Oghor-hai "Drúedain" (UT:379; this may or may not be pure Black Speech)
olog a variety of Troll apparently developed by Sauron. Olog-hai "Olog-people".
pushdug (DBS) "dungfilth", possibly push+dug "dung+filth"
ronk (DBS) "pool", tentatively isolated from bagronk, q.v.
skai (DBS) interjection of contempt
sha (DBS) interjection of contempt
sharkû (DBS?) "old man"
snaga "slave" (May be DBS.) Used of lesser breeds of Orcs (WJ:390).
thrak- "bring", infinitive thrakat, only attested with suffixes: thrakatulûk "to bring them all"
u (DBS) "to"
-ûk "all", suffixed to pronominal suffixes: -ulûk, "them all"
-ul pronominal suffix "them".
-um "-ness" in burzum "darkness". uruk a great variety of Orc. According to WJ:390, Sauron probably borrowed this word "from the Elvish tongues of earlier times".
The abbreviation DBS stands for Debased Black Speech, a colloquial idiom variety of the Black Speech as used by the orcs and goblins.