Lower bounds of polynomials on values of algebraically dependent E-functions

In the paper a lower bound of the modulus of a polynomial $\left|P\left(f_{1}(\alpha),\ldots,\,f_{s}(\alpha)\right)\right|$ with integer coefficients on the values of E-functions $f_{1}(z),\ldots,f_{s}(z)$ at an algebraic point $\alpha$ is obtained, provided $P\left(f_{1}(\alpha),\ldots,\,f_{s}(\alpha)\right)\neq0$.