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There is no formula: it is a process of swapping letters in a systematic manner.
An eight-letter word cannot be made from four letters. T, I, E and S are not sufficient to make an eight-letter word without knowing what letters can be repeated and how often they are repeated. TESTIEST could work if you allow three Ts.
solitude
endeavor
A six letter work is sicker.
Machine?
3 letter work beginning with ex
splotch could work.
mijob
You should send a business letter to your boss or an associate that you work with. Business letters should be formal and polite.
The 3-letter Greek letters that start with a "p" are phi and psi. The 3-letter Greek letter that ends in a "u" is tau. Other 3-letter Greek letters are eta, rho and chi. You work it out.
If you don't have to use all the letters, then 'HOT' or 'HOST' would work.