Solve exponenital integral equation $$\frac{1}{\sqrt{2\pi}\sigma_1 }\int_x^\infty\exp(-\frac {t_1^2-1}{2\sigma_1^2})dt_1 + \frac{1}{\sqrt{2\pi}\sigma_2 }\int_x^\infty\exp(-\frac {t_2^2-1}{2\sigma_2^2})dt_2 = a $$
$$\sigma_1 , \sigma_2 \gt 0$$ 
Is there a way to solve for $x$ !?
please help

Let $X_i\sim\mathcal N(1,\sigma_i^2)$ be independent for $i=1,2$, then the expression above is
$$\mathbb P(X_1>x) + \mathbb P(X_2>x) = a. $$
After standardizing we find that
$$\Phi\left(\frac{x-1}{\sigma_1}\right) + \Phi\left(\frac{x-1}{\sigma_2}\right)=a, $$
where $\Phi$ is the distribution function of the normal distribution with $\mu=0$, $\sigma^2=1$. In terms of the error function, this is
$$\operatorname{erf}\left(\frac{x-1}{\sqrt 2\sigma_1}\right)+\operatorname{erf}\left(\frac{x-1}{\sqrt 2\sigma_2}\right)=2(1-a). $$
This equation cannot be solved analytically, but can be approximated numerically in many ways.
