Option 1
\documentclass[preview,border=12pt,12pt]{standalone}% change it to your own document class
\usepackage[a4paper,margin=2cm,landscape]{geometry}% edit it to meet your preference
\usepackage{amsmath}
\begin{document}
\abovedisplayskip=0pt\relax% don't use this line in your production
\begin{equation}
\begin{split}
E\left(y_{i}^{T}|u_{1i}\succ-x_{1i}'\beta_{1},u_{2i}\succ-x_{2i}'\beta_{2}\right)
&=\frac{\sigma}{\Psi\left(x_{1i}'\beta_{1},\tfrac{x_{2i}'\beta_{2}}{\sigma},\rho\right)}\left[\phi\left(\tfrac{x_{2i}'\beta_{2}}{\sigma}\right)\Phi\left(\tfrac{x_{1i}'\beta_{1}-\rho\tfrac{x_{2i}'\beta_{2}}{\sigma}}{\left(1-\rho^{2}\right)^{1/2}}\right)\right.\\
&\qquad + \left. \rho\phi(x_{1i}'\beta_{1})\Phi\left(\tfrac{\tfrac{x_{2i}'\beta_{2}}{\sigma}-\rho x_{1i}'\beta_{1}}{\left(1-\rho^{2}\right)^{1/2}}\right)\right]
\end{split}
\end{equation}
\end{document}
Suggestion
To make the code more readable (to make you easier to locate what you want to modify), remove the unnecessary {}
(such as replacing X_{a}^{b}
with X_a^b
) and align the equation code with a better pattern as follows.
\documentclass[preview,border=12pt,12pt]{standalone}% change it to your own document class
\usepackage[a5paper,margin=2cm,landscape]{geometry}% edit it to meet your preference
\usepackage{amsmath}
\begin{document}
\abovedisplayskip=0pt\relax% don't use this line in your production
\begin{equation}
\begin{split}
E\left(y_i^T|u_{1i}\succ-x_{1i}'\beta_1,u_{2i}\succ-x_{2i}'\beta_2\right)
&=
\frac{\sigma}{\Psi\left(x_{1i}'\beta_1,\tfrac{x_{2i}'\beta_2}{\sigma},\rho\right)}
\left[
\phi\left(\tfrac{x_{2i}'\beta_2}{\sigma}\right)
\Phi\left(\tfrac{x_{1i}'\beta_1-\rho\tfrac{x_{2i}'\beta_2}{\sigma}}{\left(1-\rho^2\right)^{1/2}}\right)
\right.\\
&
\qquad +
\left.
\rho\phi(x_{1i}'\beta_1)\Phi\left(\tfrac{\tfrac{x_{2i}'\beta_2}{\sigma}-\rho x_{1i}'\beta_1}{\left(1-\rho^2\right)^{1/2}}\right)
\right]
\end{split}
\end{equation}
\end{document}
equation
withsplit
inside helps here.