  Considered is the equation
  $$
  (T(a)+H(b))\phi=f,
  $$ where $T(a)$ and $H(b)$, $a,b\in L^\infty(\mathbb{T})$ are, respectively,
Toeplitz and Hankel operators acting on the classical Hardy spaces
$H^p(\mathbb{T})$, $1<p<\infty$. If the generating functions $a$ and $b$
satisfy the so-called matching condition [1,2],
  $$ a(t) a(1/t)=b(t)b(1/t), \, t\in \mathbb{T},
  $$ an efficient method for solving equations with Toeplitz plus Hankel
operators is proposed. The method is based on the Wiener--Hopf factorization of
the scalar functions $c(t)=a(t)b^{-1}(t)$ and $d(t)=a(t)b^{-1}(1/t)$ and allows
one to find all solutions of the equations mentioned.
