how I can solve this problem use calculator fx-991ES or fx-991ES plus

sin( X -0.36 ) + 0.353*e^(-X / 0.377) =0

answer x= 3.5

 

I don't know about your calculator, but it might have the ability to do numerical solutions.

But you can do it with any scientific calculator (or even by hand with trig and log tables) using an interative approach in just a handful of iterations.

The two obvious starting points are X=0 and X=0.36.

The first one results in

sin(-0.36) + 0.353 = 0.000726

while the second yields

0.353* e^(-.36/.377) = 0.1359

Notice that at X=0.35 the value of the expression is 0.001625, which is more than twice the value at X=0. However, X=0 is a local minima and doesn't actually touch zero, whereas there is an actual zero at X just slight greater that 0.35 (at about 3.5016).

There are a number of games you can play using trig identities and variable substitutions to tease out information, but there is analytical solution (that I am aware of).

 

Oh, and note that there are an infinite number of solutions that, as the exponential dies off (quickly) are separated by very close to 2pi.