Transform a Continuous Time Differential Equation of a Low Pass Filter to Discrete Time
The answer comes from a discrete approximation of the derivative operator.
Sometime it is called "Finite Differences".

Look at $ \frac{ y \left[ n {T}_{s} \right] - y \left[ n {T}_{s} - {T}_{s} \right] }{ {T}_{s} } $, what happens when $ {T}_{s} \to 0 $?
We got the definition of the drivative.

Now, since we sample at interval of $ {T}_{s} $ we can agree that $ y \left[ n {T}_{s} \right] = y \left[ n \right] $ and $ y \left[ n {T}_{s} - {T}_{s} \right] = y \left[ n - 1 \right] $.

Do that and you get:

$$ R C {y}' \left ( t \right ) + y \left ( y \right ) = x \left ( t \right ) \approx R C \frac{ y \left [ n \right ] - y \left [ n - 1 \right ] }{ {T}_{s} } + y \left [ n \right ] = x \left [ n \right ] $$

Now simple adjustment and you have what you need.