The key to the treatment of the resonance radiation imprisonment lies in the solution to Holstein's equation. A new method to solve Holstein's equation is proposed in this paper, which integrates the equation directly by means of operator calculation and results in a formula for the excited particles in an infinite series in an integral operator. Our study on the behavior of the high-ordercoefficients of this series leads to the success in overcoming the difficulty to obtain the sum of infinite terms, and a formula of finite terms under any given precision is acquired, which applies to the whole time scale.