You can use the law of sines, which states that the ratio between a side and the sine of the opposite angle is constant: in this triangle, we have
[tex]\dfrac{e}{\sin(E)}=\dfrac{p}{\sin(P)}=\dfrac{r}{\sin(R)}[/tex]
In this particular case, we can use the information we have about sides and angles e, r, E, R and we have
[tex]\dfrac{e}{\sin(E)}=\dfrac{r}{\sin(R)}[/tex]
Plugging the values, we have
[tex]\dfrac{e}{\sin(61)}=\dfrac{15.7}{\sin(45)}[/tex]
Solving for e, we have
[tex]e=\dfrac{15.7\sin(61)}{\sin(45)}\approx 19.41[/tex]
