Isolating Real Roots of Polynomial–Exponential Function over Algebraic Numbers

Question

Let $\mathbb{A}$ be the set of algebraic numbers and $\mathbb{A}[t]$ the set of polynomials in $t$ with coefficients in $\mathbb{A}$. Given a finite sum of $F(t)=\sum_{k}f_k(t) e^{\eta_k t}$ for pairwise distinct $\eta_k\in \mathbb{A}$ and $f_k(t)\in \mathbb{A}[t]$, how to isolate the real roots of $F(t)=0$.