If you have studied Tolkien’s attested Tengwar writings yourself, you probably won’t get anything new from this, the distribution of silmë and essë and their respective nuquerna forms have been known in theory for quite a while now and the conclusions I draw aren’t don't add anything new. However this comes up quite frequently, so I wanted to write a slightly more extensive explanation.
Silmë and essë are special in having two variant forms: a normal or upright form an one turned upside down, known by the Quenya adjective nuquerna “reversed, (lit.) under-turned”.
In the Lord of the Rings, Appendix E Tolkien tells us about their relation:
29  represented s, and 31 [k] (with doubled curl) z in those languages that required it. The inverted forms 30 [I] and 32 [,], though available for use as separate signs, were mostly used as mere variants of 29  and 31 [k], according to the convenience of writing, e.g. they were much used when accompanied by superimposed tehtar.
Many have derived a stronger claim from this, namely that silmë and essë always take their nuquerna forms when they carry a tehta. This is however largely unsupported by the attested examples from Tolkien.
Quenya and Sindarin
In the Classical Mode for Quenya and the General Mode for Sindarin silmë has its usual value s and essë is used for ss, because both languages don’t have a voiced z sound, at least not at the time of the narrative. Whether the upright or nuquerna form is used appears to be largely unsystematic and is decided “according to the convenience of writing” and not as a hard rule:
DTS 20 — Namárie (Quenya, Classical Mode)
|lassë (read lassi)||j#KF|
DTS 49 — King’s Letter, Third Version (Sindarin, General Mode)
|(b)ess [the b occurs before a line break]||wk$|
In the main Sindarin text, there actually aren’t any examples of nuquerna forms. This might be, because in the Mode of Beleriand, a full mode for Sindain, a sign commonly identified as silmë nuquerna (though possibly unrelated in origin) is used for y, so avoiding it in the General Mode when applied to Sindarin might be a measure to avoid confusion.
Addition (30. March 2021): In the post scriptum of the King’s letter (DTS 49) the word minas appears spelled with silmë nuquerna. Since the main text consistently shows upright silmë even when used with tehtar, it might be that the conditioning factor in this case is the lesser line height.
In the General Mode for English silmë and essë are used for s and z respectively. While essë occasionally shows up in its nuquerna form much like it does in the Elvish Modes, silmë is always upright:
|DTS 5||of Westmarch||W y*F1t6Ea|
|DTS 5||the histroy||@ 98%17Y`Û|
|DTS 10||this is just (`V and `B switched)||48% KF s8&1|
|DTS 10||Christmas (`V and `B switched)||Z78$1t+D|
|DTS 84||across (`N and `M switched)||zE78&;|
There are no attestations of soft c pronounced like s (e. g. peace, since) in the General Mode for English. However in the English Full mode silmë nuquerna is used for soft cs:
This suggests that the English Modes are an example of the second possibility outlined by Tolkien, namely that the nuquerna variants are “available for use as separate signs”, in this case as s and soft c respectively.
- If you are writing Quenya in the Classical Mode, you don’t need to use silmë and essë nuquerna in all instances, where they take a tehta. You certainly can do so but don’t need to adhere to this when you think something would look better otherwise. Especially with the acute and the dot there are many examples for upright silmë and essë.
- When writing Sindarin in the General Mode, it might be better to avoid silmë nuquerna due to its collision with y in the Mode of Beleriand but it might be equally acceptable to use silmë nuquerna like in the Classical Mode as attested in the post scriptum of the King’s letter. Essë and essë nuquerna can both be used interchangeably.
- When writing English in the General Mode do not use silmë nuquerna for s, it is unattested. Write s with an upright silmë in all cases and use silmë nuquerna for soft c. Essë and essë nuquerna can both be used interchangeably.