The invertibility of Toeplitz plus Hankel operators \(T(a)+H(b)\) , \(a,b\in L^\infty \) acting on \(l^p\) -spaces is studied. If the generating functions a and b satisfy the equation \(\displaystyle a(t) a(1/t)=b(t)b(1/t), \) various sufficient conditions for the invertibility and one-sided invertibility of the operators \(T(a)+H(b)\) are obtained and the corresponding inverses are constructed. Necessary conditions of one-sided invertibility are also discussed. Besides, we suggest a generalization of the above condition for the functions a and b, which allows to extend the approach used to a substantially wider class of Toeplitz plus Hankel operators.