Your equation
1604+14a**(-1)-141604*(1-e**(-1604*a))**-1
seems to be insoluble. Why?
Because (1-e**(-1604*a))**-1.
You are raising 1-e to -1604*a, and this to -1.
If you omit the unknown there, like this:
r = solve(1604+14*x**(-1)-14*1604*(1-e**(-1604))**-1, x)
You get:
0.000671398427009400
And if you omit the multiplication and you put the unknown, like this:
r = solve(1604+14*x**(-1)-14*1604*(1-e**(x))**-1, x)
You get:
No algorithms are implemented to solve equation 1604 - 22456/(1 -
(54365636569181/20000000000000)**x) + 14/x
Maybe your equation HAS solution, so you can try to wait some time (maybe a long time) to check if your equation has solution and the solution is feasible (because it can be soluble but not feasible to calculate in a 'reasonable' time).