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The following positions the labels at the ends of the axes.
plot(E,t,(x,0,15),axes_labels=['$t$ axis','$E$ axis'])
You could use the text command to position a label.
t = var('t')
E(t)=(10.40*(1-exp(-0.25*t)))^2.81
p=plot(E,t,(x,0,15),axes_labels=['','$E$ axis'])
p+=text('$t$ axis',(8,-30),color='black')
show(p)
You may also be able to use matplotlib to get what you want.
