Hi Paul,
Symbol names that start with a capital letter are reserved for WL built-in symbols, so avoid them to prevent conflicts.
ClearAll[h, b, s, k, e, a, x, c, t, j, f]
eq = h == b*s + k*e + a*x + c*t + j*f
Solve[eq, s]
(* {{s -> (h - f j - e k - c t - a x)/b}} *)
Solve[eq, f]
(* {{f -> (h - e k - b s - c t - a x)/j}} *)
Not sure what you mean by
Then, I want to specify a cases where one or all of the constant
coefficients as originally specified are no longer constant, but
variable
You can assign a value to a symbol and re-evaluate the expression.
j = 3
Solve[eq, f]
(* {{f -> 1/3 (h - e k - b s - c t - a x)}} *)