The first mention of this root was as ᴱ√TEŊE “know, understand” in the Qenya Lexicon of the 1910s where it had derivatives like ᴱQ. tenge- “know, understand, grasp” and ᴱQ. tengwe “knowledge, understanding” (QL/91). In The Etymologies of the 1930s, Tolkien instead gave {ᴹ√TEƷ >>} ᴹ√TEÑ “line, direction” with derivatives like ᴹQ. tie/N. tê “line, way” and ᴹQ. téra/N. tîr “straight, right” (Ety/TEƷ, TEÑ). However, in the original layer of composition for the Outline of Phonology (OP2) from the early 1950s, Tolkien gave √TEG for “line” and gave √TEÑ as the basis for Q. tenna “thought, notion, idea”, perhaps a restoration of its meaning from the 1910s (PE19/97).
In another entry in The Etymologies of the 1930s, Tolkien derived ᴹQ. tengwa from ᴹ✶tekmā = ᴹ√TEK “write” + the instrumental suffix ᴹ✶-mā (Ety/TEK). The foundation of this derivation is the sound change whereby voiceless stops were voiced before nasals in Ancient Quenya, thereafter nasalizing so that ᴹ✶tekmā > tegmā > teñmā > teñgwā (PE19/43). This sound change was still in effect when Tolkien wrote the initial draft of Outline of Phonology (OP2) in the early 1950s (PE19/85-66 note #79), but at some later point Tolkien revised this rule so that the nasal instead unvoiced, so that km > kʰm̌ > kƕ > kw (PE19/85), making the derivation of tengwa from the root √TEK invalid.
As pointed out by Christopher Gilson (ibid., note #79), earlier signs of this new phonetic rule can be seen Tolkien’s notes on Words, Phrases and Passages in the Lord of the Rings from the late 1950s, where he gave √TEÑ “show, sign, indicate” instead of √TEK “[written] sign” as the new root for Q. tengwa, now derived from ✶teñwā or ✶teñmā, though Tolkien briefly considered √TEWE as a possible root in drafts to these notes (PE17/44). From this point forward, Tolkien regularly mentioned √TEÑ with glosses like “indicate, signify” (WJ/394), “represent, betoken, indicate (by sign)” (VT39/15) and “indicate, mark, signify” (PE22/149). Finally, in green-ink revisions to OP2 from 1970, Tolkien added tengwa as another derivative of √TEÑ alongside Q. tenna “thought, notion, idea” as mentioned above (PE19/97 and note #139).
See the entries on √TEG “line” and √TEK “write” for parallel developments in similar roots.
This root first appeared in the Qenya Lexicon of the 1910s as ᴱ√TENE “touch, feel”, with derivatives like ᴱQ. tende “sense of touch, sense, sensation, feeling” and ᴱQ. tenya- “feel, touch” (QL/91). G. tent “toe” and G. tentha- “feel with the feet, walk on tiptoe” from the contemporaneous Gnomish Lexicon might be related (GL/70). There were then no further signs of this root for many years, except perhaps the preposition ᴹQ. ten “for” in Fíriel’s Song of the 1930s.
The root √TEN “direction” eventually reappeared in Quenya Notes (QN) from 1957 with a single derivative, adverb or preposition Q. tenna “to the object; up to, to (reach), as far as”, as in the phrase Q. tenn’ Ambar-metta “unto the ending of the world” (LotR/967). The root √TEN also appeared with gloss “end in sense of point aimed at” (vs. √MET = “finally”) along with derivatives Q. tenna “to the point, until” and Q. †tenya- “arrive, end (not at speaker’s[?] place)” in notes from the late 1950s or early 1960s (VT49/24).
In notes from 1968, √TEN was at first used for “to, arrive (at), reach” along with derivatives Q. tenna “right up to a point (of time/place); go as far as” and a verb Q. ten- “arrive, come to”, but then Tolkien changed {√TEN >>} √MEN and revised all the verb forms of {Q. ten- >>} men- (VT49/23-24). He then gave a new gloss “point” to √TEN and updated derivatives: Q. tenna “to the point” and Q. tenta- “point to, [point] out, indicate” (VT49/24). In another note associated with 1968 drafts of the Ambidexters Sentence, the root √TEN was glossed “toward” (VT49/24).
Neo-Eldarin: For purposes of Neo-Eldarin, I’d ignore Tolkien’s brief interpretation of this root as “arrive”, and stick with the meaning “(up to the) point”, consistent with its non-deleted derivatives. For “arrive”, I’d use Q. anya- from Late Notes on Verbs written in 1969, reserving √MEN for “go” (LVS).