Summary: We propose to parametrize the configuration space of one-dimensional quantum systems of \(N\) identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the Hamiltonians of the \(A_N\), \(BC_N\), \(B_N\), \(C_N\) and \(D_N\) Calogero and Sutherland models, as well as their supersymmetric generalizations, can be expressed – for arbitrary values of the coupling constants – as quadratic polynomials in the generators of a Borel subalgebra of the Lie algebra \(\text{gl}(N+1)\) or the Lie superalgebra \(\text{gl}(N+1|N)\) for the supersymmetric case. These algebras are realized by first order differential operators. This fact establishes the exact solvability of the models according to the general definition given by Turbiner, and implies that the Calogero and Jack-Sutherland polynomials, as well as their supersymmetric generalizations, are related to finite-dimensional irreducible representations of the Lie algebra \(\text{gl}(N+1)\) and the Lie superalgebra \(\text{gl}(N+1|N)\).