How to compute the exponential map of a manifold defined by constraints..

Question

Let $M \subset \mathbb{R}^n$ be a Riemannian manifold defined by $m$ constraints $$ M = \{ x \in \mathbb{R}^n \, | \, h_i(x)=0, i=1,\cdots,m \} $$ where $h_i:(x)$ are polynomials.

My question is:

Given a $p \in M$ and $v \in T_p M$, how to compute the exponential map $Exp_p(v)$ ?

Thanks in advance.