Black-Scholes Model for options pricing

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The Black-Scholes pricing formula for a European call option is given by:

$$C(S,t) = SN(d_+) - E\exp(-r(T-t))N(d_-)$$

where $S\ge0$ is the spot price, $t\le T$ is the time,$T\ge0$ is the expiry date, $E\ge0$ is the strike, and

$$d_{\pm}=\frac{\log(S/E) + (r-D\pm\frac{1}{2}\sigma^2)(T-t))}{\sigma\sqrt{T-t}}$$

where

$$N(x)=\frac{1}{\sqrt{2\pi}}\int^x_{-\infty}\exp(-\phi^2)d\phi$$

$r\ge0$ the interest rate, $D$ the dividend yield, $\sigma$ the volatility of $S$. With these assumptions, how can we show the following equation:

$$S\exp(-d_+^2/2)=E\exp(-r(T-t))\exp(-d_{-}^2/2)$$

and what is the intuition/interpretation of it?